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Friday, February 15, 2013 Version 1.0 Page - 1 F-4 Phantom II Flight Model Identification LICENSE : This document has been created by J.M. LANGERON / TOPOLO, (http://topolo.free.fr/). All the values used to model the aircraft behavior have been computed by him, like all performance charts presented here, based on data provided by the people mentioned in the CREDITS section. If you want to use these data, or part of it, please contact the author by personal message to TOPOLO on check-six forum: (http://www.checksix-forums.com/ ). CREDITS : I want to thanks particularly and Tom COOPER (ACIG.org) for his huge knowledge on military aerospace in general, the history of these aircraft in particular, and the fact that he build the working group. A. Purpose and scope The aim of this document is to identify the Flight Model, that is: Lift coefficient, Drag Coefficient and Thrust laws, for some version of the F-4 Phantom II. In this model, Lift and drag coefficient (C L and C D ) vary with Mach number and true incidence, Thrust vary with Mach number and altitude. This leads to a model of the plane allowing forecast the performances for any specific configurations. The selected versions are: - A first one representative of the late Vietnam conflict in May 1972: F-4D Block 37 with J79-GE- 15. - A second one, a non-slated F-4E, representative of the Israel-Egypt War of Attrition in 1970: F-4E Block 41 with J79-GE-17 (delivered in 1969 through Peace Echo I). - A third one representative of the Israel-Egypt Kippur War in 1973 (delivered in 1972/73 through Peace Echo IV) and of Iran-Iraq conflict: F-4E Block 50 with Mod.556 (slated) applied during production and powered by J79-GE-17. The analysez configurations are: All studied configurations are light Air-To-Air: no external tanks, 50% of internal fuel. - Configuration “A”: F-4D Blk-37 with SUU-23/A gun pod with full ammo under the centerline and four AIM-7Es. - Configuration “B”: Non Slated F-4E Blk-41 with four AIM-7Es, two AIM-9Ds and one ALQ-71/QRC- 160-1 ECM pod. - Configuration “C”: Slated F-4E Blk-50 with four AIM-7Es, two AIM-9Ds and one ALQ-71/QRC-160-1 ECM. B. Data Collection Most of the data on which model definition is based are extracted from: - TO 1F-4C,D,E-1-Flight manual - 15 August 1973 - TO 1F-4C,D,E-1-Performance data manual -15 July 1969 o Appendix A for F-4D, o Appendix B for non slated F-4E - TO 1F-4E Flight Manual-1 Feb 1979 o Appendix A for slated F-4E (TO.556) a. Dimensional Data According to NASA_TN_D-5361, the basic dimensional data of the F-4C are: Wing Span: 38.41 ft (11.71 m) Wing Area: 538.34 ft 2 (50 m 2 ) Aspect ratio (λ=l 2 /S): 2.82 Sweepback of 25% chord: 45° These values clearly show that the aspect ratio has not been computed from Wing Area. I decide to keep the aspect ratio value and to round both Span and Area Reference Area (S): 530 ft 2 (49.24 m 2 ) Wing Span: 38.66 ft (11.79 m) Aspect ratio (λ=l 2 /S): 2.82 These values will be help for all F-4 variant studied here. b. Weight and Balance. Empty Weight Also said, zero fuel weight, include oil, two equipped crew members (440 lbs) and internal gun ammunition load (F4- E). According to “Flight Manual” page 1-2, and “Performance Manual” page B1-7 for Nose Gun Ammo. Configuration “A”( F-4D Block 37): Operating Weight : 29,800 lbs (Blk-33) Configuration “B” (F-4E Block 41): Operating Weight : 31,930 lbs Internal gun munitions (639 rds). : 373 lbs Total : 32,303 lbs Configuration “C” (F-4E Block 50):

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Page 1: F-4 Phantom II Flight Model · PDF fileF-4 Phantom II Flight Model Identification Friday, February 15, 2013 – Version 1.0 Page - 2 Operating Weight : 33,000 lbs Internal gun munitions

Friday, February 15, 2013 – Version 1.0 Page - 1

F-4 Phantom II Flight Model Identification

LICENSE: This document has been created by J.M. LANGERON / TOPOLO, (http://topolo.free.fr/). All the values used to model the aircraft behavior have been computed by him, like all performance charts presented here, based on data provided by the people mentioned in the CREDITS section. If you want to use these data, or part of it, please contact the author by personal message to TOPOLO on check-six forum: (http://www.checksix-forums.com/). CREDITS: I want to thanks particularly and Tom COOPER (ACIG.org) for his huge knowledge on military aerospace in general, the history of these aircraft in particular, and the fact that he build the working group.

A. Purpose and scope

The aim of this document is to identify the Flight Model, that is: Lift coefficient, Drag Coefficient and Thrust laws, for some version of the F-4 Phantom II.

In this model, Lift and drag coefficient (CL and CD) vary with Mach number and true incidence, Thrust vary with Mach number and altitude.

This leads to a model of the plane allowing forecast the performances for any specific configurations.

The selected versions are:

- A first one representative of the late Vietnam conflict in May 1972: F-4D Block 37 with J79-GE-15.

- A second one, a non-slated F-4E, representative of the Israel-Egypt War of Attrition in 1970: F-4E Block 41 with J79-GE-17 (delivered in 1969 through Peace Echo I).

- A third one representative of the Israel-Egypt Kippur War in 1973 (delivered in 1972/73 through Peace Echo IV) and of Iran-Iraq conflict: F-4E Block 50 with Mod.556 (slated) applied during production and powered by J79-GE-17.

The analysez configurations are:

All studied configurations are light Air-To-Air: no external tanks, 50% of internal fuel.

- Configuration “A”: F-4D Blk-37 with SUU-23/A gun pod with full ammo under the centerline and four AIM-7Es.

- Configuration “B”: Non Slated F-4E Blk-41 with four AIM-7Es, two AIM-9Ds and one ALQ-71/QRC-160-1 ECM pod.

- Configuration “C”: Slated F-4E Blk-50 with four AIM-7Es, two AIM-9Ds and one ALQ-71/QRC-160-1 ECM.

B. Data Collection

Most of the data on which model definition is based are extracted from:

- TO 1F-4C,D,E-1-Flight manual - 15 August 1973 - TO 1F-4C,D,E-1-Performance data manual -15 July

1969 o Appendix A for F-4D, o Appendix B for non slated F-4E

- TO 1F-4E Flight Manual-1 Feb 1979 o Appendix A for slated F-4E (TO.556)

a. Dimensional Data According to NASA_TN_D-5361, the basic dimensional data of the F-4C are:

Wing Span: 38.41 ft (11.71 m) Wing Area: 538.34 ft

2 (50 m

2)

Aspect ratio (λ=l2/S): 2.82

Sweepback of 25% chord: 45° These values clearly show that the aspect ratio has not been computed from Wing Area. I decide to keep the aspect ratio value and to round both Span and Area Reference Area (S): 530 ft

2 (49.24 m

2)

Wing Span: 38.66 ft (11.79 m) Aspect ratio (λ=l

2/S): 2.82

These values will be help for all F-4 variant studied here.

b. Weight and Balance.

Empty Weight Also said, zero fuel weight, include oil, two equipped crew members (440 lbs) and internal gun ammunition load (F4-E).

According to “Flight Manual” page 1-2, and “Performance Manual” page B1-7 for Nose Gun Ammo.

Configuration “A”( F-4D Block 37): Operating Weight : 29,800 lbs (Blk-33) Configuration “B” (F-4E Block 41): Operating Weight : 31,930 lbs Internal gun munitions (639 rds). : 373 lbs Total : 32,303 lbs Configuration “C” (F-4E Block 50):

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F-4 Phantom II Flight Model Identification

Friday, February 15, 2013 – Version 1.0 Page - 2

Operating Weight : 33,000 lbs Internal gun munitions (639 rds). : 373 lbs Total : 33,373 lbs

Fuel Weight According to “Flight Manual” page 1-12, with JP-4 fuel at 6.5 lbs per gallon (60 degrees F)

Configuration “A”( F-4D Block 37): Fully serviced : 12,669 lbs Not Usable : 391 lbs 50% internal fuel : 6,335 lbs Usable (with 50%) : 5,944 lbs Configuration “B” (F-4E Block 41) and Configuration “C” (F-4E Block 50): Fully serviced : 12,428 lbs Not Usable : 370 lbs 50% internal fuel : 6,214 lbs Usable (with 50%) : 5,844 lbs

Load-out Weight According to “Performance Manual” page A1-6

AIM-7E (fuselage mounted) on station 3, 4, 6 and 7: 455 lbs each, 1,820 lbs

Gun Pod on station 5 (centerline point) : 1,861 lbs - SUU-23/A gun pod with full ammo : 1,739 lbs - Aero 27A Ejector Rack : 122 lbs

2 AIM-9D on station 2 : 828 lbs

- AIM-9D : 195 lbs each - LAU-7/A pylon and launchers : 438 lbs

ALQ-71/QRC-160-1 ECM pod on station 9 : 393 lbs

- ALQ-71/QRC-160-1 ECM pod : 203 lbs - Outboard pylon : 190 lbs

Configuration “A”: 4 AIM-7E : 1,820 lbs SUU-23/A+ Aero 27A : 1,861 lbs Total : 3,681 lbs Configuration “B” and “C”: 4 AIM-7E : 1,820 lbs LAU-7/A + 2xAIM-9D : 828 lbs Out Pylon + ALQ-71/QRC-160-1 : 393 lbs Total : 3,041 lbs

Gross Weight. Configuration “A”( F-4D Block 37): Zero Fuel Weight : 29,800 lbs Fuel Weight : 6,335 lbs Load Weight : 3,681 lbs Gross Weight : 39,816 lbs Configuration “B” (F-4E Block 41): Zero Fuel Weight : 32,303 lbs Fuel Weight : 6,214 lbs Load Weight : 3,041 lbs

Gross Weight : 41,558 lbs Configuration “C” (F-4E Block 50): Zero Fuel Weight : 33,373 lbs Fuel Weight : 6,214 lbs Load Weight : 3,041 lbs Gross Weight : 42,628 lbs

c. Angle of attack (AoA) The F-4 AoA indicator display to the pilot an indication of the plane incidence through an AoA Index taking values between 0 and 30 corresponding to true incidence angle between -10 and +40 degrees. (refer to Flight manual F-4C,D,E-1-S / T.O. 1F-4C-1 page 1-32)

There is no evidence that the relation between AoA index and true incidence angle is linear, but I’ll take this hypothesis.

Let’s call - AoAt the true AoA angle in degree - AoAi the AoA index value

We know AoAt(AoAi=0) = -10 deg AoAt(AoAi=30) = +40 deg

This gives the following relation (B.d.1)

Approach AoA index is said to be 19.2, so 22 degree of true AoA angle

Optimum cruise is got for an AoA index of 7.9, leading us to say that the maximum lift to drag ratio is reached for a true incidence angle of 3.2 degrees.

Minimum drag (or zero lift) is said to be reached for an index of 5 units (page 6-1) that does fit to a true incidence angle of -1.6 degrees).

d. Speed limitations. Independently of external loads, speed limitation of the clean aircraft are described in Flight manual F-4C,D,E-1-S page 5-5

- IAS below 750Kts for altitude below 30,000ft - IAS below 700Kts for altitude above 30,000ft - Mach number below 2.4 (and below 2.0 for normal

usage)

External store speed limitations are described page 5-13 and following of the flight manual. Those involved in our selected configurations are the followings:

- AIM-7E : None, assuming warhead is not an MK 18.

- SUU-23/A : None - AIM-9D : No limitations, assuming MK 8 Mod 3

warhead are used

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- ALQ-71/QRC-160-1 : described page 5-61, due to pod’s RAT limitation, 750Kts up to 25,000ft, 650Kts at 40,000ft (with linear variation between, i.e.

),

and mach number below 2.0 (above 40,000ft)

Configuration “A” has no additional speed limitations due to external loads, when configuration “B” and “C” support ALQ-71 ART limits

e. Load Factor limitations. In any case, negative load factor is limited as follow (ref. Flight manual F-4C,D,E-1-S page 5-4)

- No more than 30s of negative G flight - No more than 10s of zero G flight

In general, load factor limits depend on: external stores, Mach number and gross weight, as described on top of page 5-10 (figure 5.8)

Variation along Mach number is assumed to be:

- Constant for Mach number < 0.72 : N1(GW) - Constant for Mach number > 1.05 : N2(GW) - Linear for Mach number in [0.72 ; 1.05] :

That means that, for each configuration (A, B, C and clean) we have to extract from figure 5.8 the subsonic and supersonic load factor limit according to their gross weight and external stores:

Configuration “A” or Clean Depending on gross Weight the N1 and N2 values are:

- GW < 37,500 lbs : N1 = 8.5G - GW > 58,000 lbs : N1 = 5.5G - GW in [37,500 ; 58,000]

- GW < 37,500 lbs : N2 = 6.5G - GW > 58,000 lbs : N2 = 4.2G - GW in [37,500 ; 58,000]

Configuration “B” or “C” No difference between subsonic and supersonic load factor limits, it does depend only on Gross Weight

- GW < 37,500 lbs : N = 6G - GW > 58,000 lbs : N = 3.9G - GW in [37,500 ; 58,000]

f. External loads Drag. Then we will determine the external loads drag impact in defining the law that links Drag Index to drag coefficient.

External load Drag Index. According to “Performance Manual” page A1-6

AIM-7E (fuselage mounted) on station 3, 4, 6 and 7: 1.3 each, 5.2 for all

Gun Pod on station 5 (centerline point) : 12.0 - SUU-23/A gun pod with full ammo : 8.1 - Aero 27A Ejector Rack : 3.9

2 AIM-9D on station 2 : 6.0

- AIM-9D : 1.3 each - LAU-7/A pylon and launchers : 3.4

ALQ-71/QRC-160-1 ECM pod on station 9 : 4.1

- ALQ-71/QRC-160-1 ECM pod : 2.0 - Outboard pylon : 2.1

Configuration “A”: 4 AIM-7E : 5.2 SUU-23/A+ Aero 27A : 12.0 Total : 17.2 Configuration “B” and “C”: 4 AIM-7E : 5.2 LAU-7/A + 2xAIM-9D : 6.0 Out Pylon + ALQ-71/QRC-160-1 : 4.1 Total : 15.3

Drag Index impact determination. As a basis, we assume that the Drag coefficient is known for a given Drag Index value (DI0) and that the Drag coefficient for any Drag Index value is given by:

(B.j.1) CD(DI) = CD(DI0) + (DI - DI0).k

We also assume that the value of (k) is not constant along Mach number, in fact we will use a (k1) value for Mach number in [0;0.9], another (k2) value for Mach number in [1.0;..[ , and a linear interpolation in between.

Based on other aircraft analysis we can propose

k2 =2.00. k1

The determination of (k1) value can be based on the assumption that each Drag index point corresponds to a Drag force increase of 1%, and then compared to the induced time increase on level flight acceleration schedule. Based on the previous hypothesis, we will take :

k1 =0.000181

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C. Data recognition

Define Thrust and Drag coefficient versus AoA. It would have been possible to determine Thrust laws (thrust force at maximum A/B or military power from Mach number and altitude) independently from the general Drag coefficient laws if we restrict to the portion of the flight domain where incidence is small enough to approximate drag by null-lift drag, and is these portion are documented, either by acceleration schedule (speed along time) or Extra specific power tables.

On the opposite, the available data in Performance data manual describe (pages number identified for F-4C/D, but same data also exist for F-4E):

- Accurate acceleration schedule from Mach 0.5 to 0.9 for altitude between sea level and 6,000ft (page A9-26)

- Rough acceleration schedule from M0.6 to 1.4 at 10,000ft (page A9-37)

- Rough acceleration schedule from M0.8 to 1.9 at 30,000ft (page A9-38)

- Rough acceleration schedule from M1.0 to 2.05 at 35,000ft, 40,000ft and 45,000ft (pages A9-39, 40 and 41)

- Maximum reachable speed along altitude (level flight envelope, page A9-89)

- Sustained load factor, turn rate and turn radius from stall speed to maximum speed at sea level, 10,000ft, 20,000ft, 35,000ft and 45,000ft. (page A9-102)

So, the proposed methodology is the following:

1- Forecast a simple Drag versus Lift law. 2- From the sea level acceleration schedule and

maximum reachable speed (level flight envelope figure), we compute the Extra-specific Power (Ps) for every Mach number between 0.5 and 0.9, and deduce thrust values Mach number over 0.5. This will also give us the maximum Lift coefficient value (CL1) for which the Drag law has an impact on the acceleration schedule.

3- Smooth Thrust curves in fitting acceleration schedule more than Ps values

4- Tune Drag law up to lift required for level flight at M0.5 (CL1) using sustained turn rate curves at sea level.

5- Based on sustained turn rate curves, propose a thrust law for Mach number under 0.5 and a Drag law for incidence up to maximum.

6- Use rough acceleration schedule, sustained turn rate and maximum level flight speed at 10,000ft to build the 10,000ft Thrust curve.

7- Iterate between steps 3, 4, 5 and 6 to fit available data with an acceptable error margin.

At this step, we will have:

Thrust curve at Sea Level and 10,000ft from Mach 0.2 (minimum speed at SL) to 1.3/1.4 (maximum speed at FL100)

Drag versus AoA law for Mach number under 1.4 (we assume it not depending on altitude).

8- Use rough acceleration schedule, sustained turn rate and maximum level flight speed at 35,000ft to build a Thrust curve and Drag versus AoA law for mach number over 1.4.

9- Use sustained turn rate and maximum level flight speed at 20,000ft to build a Thrust curve.

10- Use rough acceleration schedule and maximum level flight speed at 30,000ft to build a Thrust curve.

11- Use rough acceleration schedule, sustained turn rate and maximum level flight speed at 45,000ft to build a Thrust curve.

12- Use minimum and maximum speed at 50,000 ft from level flight envelope to build a thrust curve.

13- Define thrust at 60,000ft and higher to respect ceiling value from level flight envelope

During all these steps we will use the following relations and definitions:

- Thrust (Max A/B) is depending on altitude and Mach number, nothing else.

- Drag coefficient (CD) depends on Mach number (M) and AoA through Lift coefficient (CL).

CD(M,AoA) = CD0(M) + k1(M)*(max(0;CL-CL1(M)))2

+ k2(M)*( max(0;CL-CL2(M)))2

+ k3(M)*( max(0;CL-CL3(M)))2

CD0(Mach) being described in §B.c CL(Mach,AoA) being described in §B.e

For a level flight, the relation between Thrust (Th), Extra Specific Power (Ps), Lift and Drag coefficient are:

With - Th, thrust in N (Newton) - V, true air speed in m/s, - Ps, Extra specific power in m/s - Vz, vertical speed in m/s, - m, mass in Kg - g = 9.81 m/s

2

combined with

gives

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- For a sustained turn flight, the relation between Thrust (Th), Load factor (Ng), Lift and Drag coefficient is:

(B.f.4)

With - z, altitude - M, mach number, - A(z), sound speed in m/s at altitude z, - ρ(z), air density in Kg/m

3 at altitude z,

- S, reference area in m2.

AoA limitations The incidence limitation will be deduced from the V-N envelope diagram.

When we speak about incidence limitations, they are not values that have to be respected by the pilot (like VNE for speed, or loaf factor), but maximum incidence values that can reach the plane due to the lack of efficiency of the pitch command devices, occurring in trans or supersonic conditions.

A diagram determines a unique value of the altitude and gross weight.

For every CAS value, we can compute the Mach number, then we read from the diagram the maximum reachable load factor (Ng) and transform it into the corresponding Lift Coefficient value, last we find the incidence that combined with the Mach number offer the required Lift Coefficient value according the CL(Mach,AoA) laws defined in the section “Lift coefficient versus AoA”.

a. F-4D (J79-GE-15)

Null lift Drag coefficient The null lift drag coefficient is assumed to be dependent on two variables: Mach number and Drag Index (that represents the impact of the external loads).

In a first step we will define the null lift drag coefficient for a clean aircraft (no external load) along Mach number using NASA_CR-2144 page 12 figure.

Mach Number Null Lift Drag Coefficient

M < 0.85 0.0181

1.00 0.0399

1.19 0.0449

1.55 < M < 1.84 0.0423

2.00 0.0406

2.50 0.0378

Lift coefficient vesurs AoA Data extracted from “Performance data manual F-4C,D,E-1-1-S” pages A9-92 to A9-95

These data are assumed to describe the relation between AoA and load factor without taking into account the contribution of the engine thrust to the lift (contribution of full after burner engines at a true AoA angle of 40degrees cannot be neglected.), so we will use the relation:

The subsonic lift coefficient law will be defined from data of page A9-92, A9-93

- SL at M0.5/330Kts CAS (+)

- SL At M0.697/460Kts CAS(X)

AoA

units

AoA

AngleNg CL(Ng)

0 -10.00 -0.60 -0.1146

2 -6.67 0.00 0.0000

4 -3.33 0.60 0.1146

6 0.00 1.10 0.2102

8 3.33 1.80 0.3439

10 6.67 2.30 0.4394

12 10.00 3.00 0.5732

14 13.33 3.30 0.6305

16 16.67 3.70 0.7069

18 20.00 4.00 0.7642

20 23.33 4.30 0.8215

30 40.00 5.20 0.9935

AoA

units

AoA

AngleNg CL(Ng)

0 -10.00 -1.20 -0.1180

2 -6.67 0.00 0.0000

4 -3.33 1.00 0.0983

6 0.00 2.10 0.2065

8 3.33 3.20 0.3146

10 6.67 4.35 0.4277

12 10.00 5.40 0.5310

14 13.33 6.35 0.6244

16 16.67 7.10 0.6981

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- 20,000ft M0.643/300Kts CAS (o)

So if we compare to lift coefficient (CL) laws is defined by:

- Null lift for AoA angle equal to -6.67 deg. - CL(AoAT) is linear up to 10deg with a value of 0.55 - CL max is equal to 1.00, reached for an AoA of 40

deg.

We get the following figure:

- Solid line : (CL) law - (+) Page A9-92, Sea level 330Kts CAS - (X) Page A9-92, Sea level 330Kts CAS - (o) Page A9-93, 20,000ft 300Kts CAS

If we apply the same method to determine the lift coefficient law for Mach number between 0.85 and 0.95 in using:

- Page A9-93, 20,000ft, 430Kts CAS/M0.908 (+) - Page A9-92, sea-level, 600Kts CAS/M0.909 (x) - Page A9-94, 30,000ft, 350Kts CAS/M0.9 (o).

We have to assume that Max load factor is not reached for a incidence angle of 40deg, but much more probably for an incidence angle of 24, in that case, the comparison figure with

- Null lift for AoA angle equal to -6.67 deg. - CL(AoAT) is linear up to 10deg with a value of 0.60 - CL max is equal to 1.00, reached for an AoA of 40

deg.

Following same method to determine the lift coefficient law for Mach number between 1.00 and 1.10 in using:

- Page A9-92, sea-level, 700Kts CAS/M1.061 (o) - Page A9-93, 20,000ft, 500Kts CAS/M1.056 (x) - Page A9-94, 30,000ft, 400Kts CAS/M1.030 (+).

Lift coefficient (CL) laws is defined by

- Null lift for AoA angle equal to -5.00 deg. - CL(AoAT) is linear up to 10deg with a value of 0.55 - CL max of 1.02, reached for an AoA of 40 deg.

Following same method to determine the lift coefficient law for Mach number between 1.15 and 1.25 in using:

- Page A9-93, 20,000ft, 570Kts CAS/M1.215 (x) - Page A9-94, 30,000ft, 460Kts CAS/M1.206 (+). - Page A9-95, 40,000ft, 380Kts CAS/M1.193 (o)

Lift coefficient (CL) laws is defined by

- Null lift for AoA angle equal to -3.50 deg. - CL(AoAT) is linear up to 20deg with a value of 0.70 - CL max of 1.02, reached for an AoA of 40 deg.

AoA

units

AoA

AngleNg CL(Ng)

0 -10.00 -0.60 -0.1510

2 -6.67 -0.10 -0.0252

4 -3.33 0.40 0.1007

6 0.00 0.80 0.2014

8 3.33 1.35 0.3398

10 6.67 1.90 0.4783

12 10.00 2.30 0.5789

-0.3000

-0.2000

-0.1000

0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.0000

1.1000

-10.00 0.00 10.00 20.00 30.00 40.00

CL(AoA) Mach in [0.0;0.8]

-0.3000

-0.2000

-0.1000

0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.0000

1.1000

-10.00 0.00 10.00 20.00 30.00 40.00

CL(AoA) Mach in [0.85;0.95]

-0.3000

-0.2000

-0.1000

0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.0000

1.1000

-10.00 0.00 10.00 20.00 30.00 40.00

CL(AoA) Mach in [1.0;1.1]

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Following same method to determine the lift coefficient law for Mach number between 1.25 and 1.35 in using:

- Page A9-93, 20,000ft, 610Kts CAS/M1.300 (+) - Page A9-94, 30,000ft, 500Kts CAS/M1.308 (x). - Page A9-95, 40,000ft, 420Kts CAS/M1.316 (o)

Lift coefficient (CL) laws is defined by

- Null lift for AoA angle equal to -3.33 deg. - CL(AoAT) is linear up to 10deg with a value of 0.37 - CL max of 1.00, reached for an AoA of 40 deg.

Following same method to determine the lift coefficient law for Mach number between 1.35 and 1.45 in using:

- Page A9-93, 20,000ft, 660Kts CAS/M1.400 (+) - Page A9-94, 30,000ft, 540Kts CAS/M1.399 (x). - Page A9-95, 40,000ft, 450Kts CAS/M1.415 (o)

Lift coefficient (CL) laws is defined by

- Null lift for AoA angle equal to -4.00 deg. - CL(AoAT) is linear up to 40deg with a value of 1.04

Following same method to determine the lift coefficient law for Mach number between 1.45 and 1.55 in using:

- Page A9-93, 20,000ft, 710Kts CAS/M1.500 (+) - Page A9-94, 30,000ft, 590Kts CAS/M1.512 (x). - Page A9-95, 40,000ft, 480Kts CAS/M1.514 (o)

Lift coefficient (CL) laws is defined by

- Null lift for AoA angle equal to -5.00 deg. - CL(AoAT) is linear up to 40deg with a value of 1.04

Following same method to determine the lift coefficient law for Mach number between 1.95 and 2.05 in using:

- Page A9-95, 40,000ft, 650Kts CAS/M2.00 (o)

Lift coefficient (CL) laws is defined by

- Null lift for AoA angle equal to -5.30 deg. - CL(AoAT) is linear up to 40deg with a value of 1.32

-0.3000

-0.2000

-0.1000

0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.0000

1.1000

-10.00 0.00 10.00 20.00 30.00 40.00

CL(AoA) Mach in [1.15;1.25]

-0.3000

-0.2000

-0.1000

0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.0000

1.1000

-10.00 0.00 10.00 20.00 30.00 40.00

CL(AoA) Mach in [1.25;1.35]

-0.3000

-0.2000

-0.1000

0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.0000

1.1000

-10.00 0.00 10.00 20.00 30.00 40.00

CL(AoA) Mach in [1.35;1.45]

-0.2000

-0.1000

0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.0000

1.1000

-10.00 0.00 10.00 20.00 30.00 40.00

CL(AoA) Mach in [1.45;1.55]

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If we look globally on the variation of CL along Mach number for a given AoA angle, we get the following kind of curves:

AoA limitations Data extracted from “Performance data manual F-4C,D,E-1-1-S” page A9-95.

CAS Mach Ng CL(Ng) AoA CL

(AoA) Error

200 0.66 1.80 1.0537 40.00 1.0000 5.10%

300 0.78 3.80 1.0074 40.00 1.0000 0.74%

250 0.81 2.55 1.0013 40.00 1.0000 0.13%

300 0.96 3.55 0.9995 40.00 1.0057 -0.63%

350 1.10 4.85 1.0269 40.00 1.0200 0.67%

400 1.25 5.60 0.9261 32.00 0.9316 -0.59%

450 1.42 5.40 0.6958 25.50 0.6984 -0.38%

500 1.57 5.00 0.5228 16.70 0.5212 0.30%

550 1.71 5.15 0.4524 12.50 0.4531 -0.14%

600 1.86 5.35 0.4004 9.50 0.4035 -0.77%

650 2.00 5.50 0.3549 6.85 0.3540 0.26%

If we except the first measure point at 200Kts (CAS), we get AoA limitations fitting with Load factor with a less than 1% error.

The AoA limitation (in true AoA, not index) along mach number is represented with the following figure:

Thrust and Drag coefficient versus AoA At sea level, we have both acceleration schedule (Mach number along time from M0.5) and Sustained load factor and turn rate. These two last values are related (for a give true speed) by physic relation that allow to reduce graphical error: load factor and turn rate are extracted from graphic curves, then turn rate is computed from the load factor, and the assumed turn rate value is the average between the extracted one and the one computed from the load factor.

Acceleration schedule is computed (forecasted) by integration of acceleration along 180s of flight.

For each value the difference between the extracted value end the forecasted one is computed: a green cell means an error of less than 2%, a yellow between 2 and 5%.

This lead to the following graphics and tables:

Turn rates at M0.9 and M1.0 are limited by structural limits of the plane and so are not true maximum sustained turn rates.

-0.3000

-0.2000

-0.1000

0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.0000

1.1000

1.2000

1.3000

1.4000

-10.00 0.00 10.00 20.00 30.00 40.00

CL(AoA) Mach in [1.95;2.05]

0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.0000

1.1000

1.2000

1.3000

1.4000

0.00 0.50 1.00 1.50 2.00 2.50

CL (AoA=Cst;Mach)

CL Max

CL(AoA=25)

CL(AoA=12)

0.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

40.00

45.00

0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0

AoA Max (mach)

0.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

16.00

0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10

Sustained Turn Rate from Table Computed

Alt Mach CAS Tr Ng Tr(Ng) Average

0 0.30 198 6.75 1.60 6.88 6.81 6.68 -1.97% 8.31 45.42

0 0.40 264 10.75 2.90 11.24 11.00 11.04 0.40% 8.31 34.07

0 0.50 330 12.40 4.00 12.79 12.60 12.35 -1.99% 8.31 27.25

0 0.60 396 13.40 4.90 13.21 13.30 13.20 -0.74% 8.31 22.71

0 0.70 462 13.90 5.90 13.72 13.81 13.56 -1.82% 8.31 19.47

0 0.80 528 14.00 6.95 14.20 14.10 14.09 -0.08% 7.84 16.05

0 0.90 594 13.50 7.24 13.17 13.33 13.17 7.24 13.17

0 1.00 660 12.50 6.65 10.86 11.68 10.86 6.65 10.86

0 1.10 726 9.75 4.90 7.20 8.48 8.23 -2.92% 6.35 9.42

Sustained Turn Rate (4xAIM-7 - 38,796lbs- AA2)

Raw from Diagram CleanedComputed Error Ng Limit

Tr

(NgMax)

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At 10,000ft, following the same schema:

Sustained turn rates and load factor

Acceleration from Mach 0.6

At 20,000ft, we have only sustained turn rates and load factor, no acceleration schedule:

At 30,000ft, we have only the acceleration schedule from Mach 0.9, no sustained turn rates nor load factor:

0.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00

0.0 5.0 10.0 15.0 20.0

Mach (time) from Table Computed

From Table Computed

Alt Mach CAS Time(min) Time (s) M(time)

0 0.50 330 0.00 0.0 0.50 0.00%

0 0.55 363 0.04 2.4 0.55 0.69%

0 0.60 396 0.08 4.8 0.61 1.04%

0 0.65 429 0.12 7.2 0.66 1.11%

0 0.70 462 0.16 9.6 0.71 0.95%

0 0.75 495 0.20 12.0 0.76 0.77%

0 0.80 528 0.24 14.4 0.81 0.75%

0 0.85 561 0.27 16.2 0.84 -0.66%

0 0.90 594 0.31 18.6 0.89 -0.61%

Error

Acceleration level flight (4xAIM-7-40,000lbs-AG2)

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.00

11.00

12.00

0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40

Sustained Turn Rate from Table Computed

Alt Mach CAS Tr Ng Tr(Ng) Average

10,000 0.30 165 2.00 1.25 4.28 3.14 3.15 0.23% 8.31 47.07

10,000 0.40 220 7.25 2.10 7.90 7.58 7.50 -0.96% 8.31 35.30

10,000 0.50 275 9.00 2.80 8.95 8.98 8.94 -0.36% 8.31 28.24

10,000 0.60 331 9.60 3.50 9.57 9.58 9.75 1.71% 8.31 23.53

10,000 0.70 387 10.10 4.30 10.23 10.16 10.37 2.00% 8.31 20.17

10,000 0.80 443 10.25 5.00 10.48 10.37 10.51 1.41% 7.84 16.63

10,000 0.90 499 10.25 5.60 10.48 10.36 10.50 1.26% 7.24 13.64

10,000 1.00 555 9.25 5.60 9.43 9.34 9.31 -0.33% 6.65 11.25

10,000 1.10 613 7.75 5.25 8.02 7.88 7.88 -0.08% 6.35 9.76

10,000 1.20 671 6.10 4.50 6.26 6.18 6.10 -1.29% 6.35 8.95

10,000 1.30 728 4.75 3.90 4.96 4.86 4.66 -4.05% 6.35 8.26

10,000 1.40 784 0.00 1.00 0.00 0.00 0.00 6.35 7.67

Sustained Turn Rate (4xAIM-7 - 38,796lbs- AA2)

Raw from Diagram CleanedComputed Error Ng Limit

Tr

(NgMax)

0.60

0.70

0.80

0.90

1.00

1.10

1.20

1.30

1.40

0 10 20 30 40 50 60 70 80 90 100 110 120 130

Mach (time) from Table Computed

From Table Computed

Alt Mach CAS Time(min) Time (s) M(time)

10,000 0.60 331 0.0 0.60 0.00%

10,000 0.70 387 5.2 0.69 -1.12%

10,000 0.80 443 10.4 0.78 -2.10%

10,000 0.90 499 15.6 0.87 -2.91%

10,000 1.00 555 23.0 0.98 -1.59%

10,000 1.10 613 33.6 1.09 -0.74%

10,000 1.20 671 46.2 1.19 -1.00%

10,000 1.30 728 64.6 1.29 -0.81%

10,000 1.35 756 81.8 1.34 -0.37%

10,000 1.40 784 122.8 1.39 -0.56%

Acceleration level flight (4xAIM-7-40,000lbs-AG2)

Error

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70

Sustained Turn Rate from Table Computed

Alt Mach CAS Tr Ng Tr(Ng) Average

20,000 0.30 138 0.00 0.00 0.00 8.31 48.91

20,000 0.40 184 3.50 1.30 3.69 3.60 3.61 0.37% 8.31 36.68

20,000 0.50 230 5.60 2.00 6.16 5.88 5.83 -0.78% 8.31 29.35

20,000 0.60 279 6.50 2.40 6.47 6.48 6.49 0.15% 8.31 24.45

20,000 0.70 328 7.00 3.00 7.19 7.09 7.17 1.02% 8.31 20.96

20,000 0.80 377 7.25 3.40 7.22 7.24 7.26 0.29% 7.84 17.28

20,000 0.90 426 7.50 4.00 7.65 7.58 7.51 -0.82% 7.24 14.18

20,000 1.00 475 7.00 4.10 7.07 7.04 7.06 0.38% 6.65 11.69

20,000 1.10 519 6.40 4.00 6.26 6.33 6.32 -0.10% 6.35 10.15

20,000 1.20 563 5.60 3.90 5.59 5.59 5.59 -0.09% 6.35 9.30

20,000 1.30 610 5.00 3.80 5.02 5.01 5.01 0.03% 6.35 8.59

20,000 1.40 660 4.30 3.70 4.53 4.41 4.41 0.03% 6.35 7.97

20,000 1.50 710 3.50 3.20 3.60 3.55 3.55 -0.06% 6.35 7.44

20,000 1.60 758 2.00 2.20 2.18 2.09 2.05 -1.93% 6.35 6.98

Sustained Turn Rate (4xAIM-7 - 38,796lbs- AA2)

Raw from Diagram CleanedComputed Error Ng Limit

Tr

(NgMax)

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At 35,000ft:

At 45,000ft:

0.80

1.00

1.20

1.40

1.60

1.80

2.00

2.20

0 30 60 90 120 150 180 210 240

Mach (time) from Table Computed

From Table Computed

Alt Mach CAS Time(min) Time (s) M(time)

30,000 0.80 308 0.0 0.80 0.00%

30,000 1.00 390 22.3 1.00 -0.37%

30,000 1.20 458 56.9 1.22 1.42%

30,000 1.40 541 85.6 1.40 -0.20%

30,000 1.60 626 119.2 1.59 -0.82%

30,000 1.80 708 166.4 1.79 -0.54%

Acceleration level flight (4xAIM-7-40,000lbs-AG2)

Error

0.00

1.00

2.00

3.00

4.00

5.00

0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00

Sustained Turn Rate from Table Computed

Alt Mach CAS Tr Ng Tr(Ng) Average

35,000 0.30 99 0.00 0.00 0.00 8.31 52.12

35,000 0.40 132 0.00 0.00 0.00 8.31 39.09

35,000 0.50 165 0.00 0.00 0.00 8.31 31.27

35,000 0.60 202 2.25 1.30 2.62 2.44 2.44 0.16% 8.31 26.06

35,000 0.70 239 3.20 1.50 3.03 3.11 3.14 0.88% 8.31 22.34

35,000 0.80 276 3.60 1.80 3.55 3.57 3.52 -1.39% 7.84 18.41

35,000 0.90 313 4.00 2.10 3.89 3.94 3.94 -0.12% 7.24 15.11

35,000 1.00 350 3.90 2.30 3.93 3.91 3.90 -0.25% 6.65 12.46

35,000 1.10 384 3.70 2.40 3.76 3.73 3.70 -0.81% 6.35 10.81

35,000 1.20 418 3.55 2.45 3.53 3.54 3.58 1.22% 6.35 9.91

35,000 1.30 453 3.40 2.50 3.34 3.37 3.40 0.81% 6.35 9.15

35,000 1.40 489 3.25 2.60 3.25 3.25 3.31 1.86% 6.35 8.50

35,000 1.50 525 3.10 2.70 3.17 3.13 3.18 1.52% 6.35 7.93

35,000 1.60 564 3.00 2.75 3.03 3.02 2.97 -1.65% 6.35 7.43

35,000 1.70 603 2.90 2.80 2.92 2.91 2.91 0.13% 6.35 7.00

35,000 1.80 642 2.50 2.80 2.75 2.63 2.60 -1.20% 6.35 6.61

35,000 1.90 681 2.00 2.30 2.07 2.03 2.00 -1.42% 6.35 6.26

Sustained Turn Rate (4xAIM-7 - 38,796lbs- AA2)

Raw from Diagram CleanedComputed Error Ng Limit

Tr

(NgMax)

1.00

1.20

1.40

1.60

1.80

2.00

2.20

0 30 60 90 120 150 180 210 240

Mach (time) from Table Computed

From Table Computed

Alt Mach CAS Time(min) Time (s) M(time)

35,000 1.00 350 0.0 1.00 0.00%

35,000 1.20 418 42.0 1.22 1.42%

35,000 1.40 489 76.0 1.40 0.25%

35,000 1.60 564 111.0 1.60 -0.26%

35,000 1.80 642 147.0 1.81 0.64%

35,000 1.90 681 163.0 1.89 -0.29%

Acceleration level flight (4xAIM-7-40,000lbs-AG2)

Error

0.00

1.00

2.00

0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00

Sustained Turn Rate from Table Computed

Alt Mach CAS Tr Ng Tr(Ng) Average

45,000 0.30 78 0.00 0.00 0.00 8.31 52.38

45,000 0.40 104 0.00 0.00 0.00 8.31 39.29

45,000 0.50 130 0.00 0.00 0.00 8.31 31.43

45,000 0.60 160 0.00 0.00 0.00 8.31 26.19

45,000 0.70 190 0.00 0.00 0.00 8.31 22.45

45,000 0.80 220 1.00 1.10 1.09 1.05 1.07 1.96% 7.84 18.51

45,000 0.90 250 1.75 1.30 1.76 1.75 1.74 -0.99% 7.24 15.18

45,000 1.00 280 1.80 1.40 1.87 1.83 1.88 2.69% 6.65 12.53

45,000 1.10 312 1.80 1.45 1.82 1.81 1.82 0.49% 6.35 10.87

45,000 1.20 344 1.80 1.51 1.80 1.80 1.80 0.12% 6.35 9.96

45,000 1.30 376 1.80 1.57 1.77 1.79 1.76 -1.64% 6.35 9.20

45,000 1.40 408 1.75 1.63 1.75 1.75 1.75 0.03% 6.35 8.54

45,000 1.50 440 1.70 1.69 1.73 1.72 1.72 0.49% 6.35 7.97

45,000 1.60 470 1.50 1.75 1.71 1.60 1.60 -0.47% 6.35 7.47

45,000 1.70 500 1.50 1.81 1.69 1.60 1.60 0.15% 6.35 7.03

45,000 1.80 530 1.50 1.80 1.58 1.54 1.54 -0.07% 6.35 6.64

45,000 1.90 560 1.25 1.60 1.25 1.25 1.19 -5.18% 6.35 6.29

45,000 2.00 590 0.50 1.10 0.44 0.47 0.89 6.35 5.98

Sustained Turn Rate (4xAIM-7 - 38,796lbs- AA2)

Raw from Diagram CleanedComputed Error Ng Limit

Tr

(NgMax)

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1.00

1.20

1.40

1.60

1.80

0 30 60 90 120 150 180 210 240 270

Mach (time) from Table Computed

From Table Computed

Alt Mach CAS Time(min) Time (s) M(time)

45,000 1.00 280 0.0 1.00 0.00%

45,000 1.10 312 50.8 1.10 -0.43%

45,000 1.20 344 102.4 1.20 0.02%

45,000 1.30 376 153.4 1.32 1.39%

Acceleration level flight (4xAIM-7-40,000lbs-AG2)

Error

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g. F-4E (J79-GE-17) without slats (TO.556 not applied)

Null lift Drag coefficient These coefficient are assumed to be exactly the same as the one of the F-4D, first because we assume there are few aerodynamic differences between the two version (if we except the impact of the internal gun), and secondly because it’s quite impossible to differentiate impact of the thrust increase (from J79-GE-15 to GE-17) from the one of a possible drag increase.

Lift coefficient versus AoA If we have assumed that the drag is the same, we should consider the same for lift. Nevertheless, we have re-computed Lift coefficient from the available V/N diagrams and, at the end, find values very close to the one of the F-4D.

Data extracted from “Performance data manual F-4C,D,E-1-1-S”, version issued 15

th July of 1969, Appendix “B” related

to non slated versions, pages B9-75 to A9-78 (Appendix “C” related to slated version is missing)

Following the same methodology, here are the CL curves for different Mach ranges:

In the figure above, the solid curve is computed with the same law than the one used for F-4D:

- Null lift for AoA angle equal to -6.67 deg. - CL(AoAT) is linear up to 10deg with a value of 0.55 - CL max is equal to 1.00, reached for an AoA of 40

deg.

Other symbols (x), (+), (o) are values extracted from diagram at 5,000ft for 300 and 450Kts (p. B9-75), 20,000ft and 300Kts (p. B9-76) and 30,000ft at 300Kts (p B9-77).

All values show that F-4E wing without slats provide the same lift than the F-4D one.

In the figure above, the solid curve is the one following the law:

- Null lift for AoA angle equal to -6.67 deg. - CL(AoAT) is linear up to 12deg with a value of 0.63 - CL max is equal to 0.95, reached for an AoA of 40

deg.

Other symbols (x), (+), (o) are values extracted from diagram at 5,000ft for 550Kts (p. B9-75), 20,000ft and 430Kts (p. B9-76) and 30,000ft at 350Kts (p B9-77).

The lift is to be considered as a bit lower than the one measured on an F-4D.

In the figure above, the solid curve is the one following the law:

- Null lift for AoA angle equal to -6.67 deg. - CL(AoAT) is linear up to 10deg with a value of 0.55 - CL max is equal to 1.00, reached for an AoA of 40

deg.

-0.2000

-0.1000

0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.0000

1.1000

-10.00 0.00 10.00 20.00 30.00 40.00

CL(AoA) Mach in [0.0;0.8]

-0.3000

-0.2000

-0.1000

0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.0000

1.1000

-10.00 0.00 10.00 20.00 30.00 40.00

CL(AoA) Mach in [0.85;0.95]

-0.3000

-0.2000

-0.1000

0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.0000

1.1000

-10.00 0.00 10.00 20.00 30.00 40.00

CL(AoA) Mach in [1.0;1.1]

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Other symbols (x), (+), (o) are values extracted from diagram at 5,000ft for 640Kts (p. B9-75), 20,000ft and 500Kts (p. B9-76) and 30,000ft at 400Kts (p B9-70).

In the figure above, the solid curve is the one following the law:

- Null lift for AoA angle equal to -3.50 deg. - CL(AoAT) is linear up to 24deg with a value of 0.93 - CL max is equal to 1.03, reached for an AoA of 40

deg.

Other symbols (x), (+), (o) are values extracted from diagram at 20,000ft and 570Kts (p. B9-76), 30,000ft at 460Kts (p B9-77) and 40,000ft and 380Kts (p. B9-78)

In the figure above, the solid curve is the one following the law:

- Null lift for AoA angle equal to -1.60 deg. - CL(AoAT) is linear up to 20deg with a value of 0.70 - CL max is equal to 1.00, reached for an AoA of 40

deg.

Other symbols (x), (+), (o) are values extracted from diagram at 20,000ft and 610Kts (p. B9-76), 30,000ft at 500Kts (p B9-77) and 40,000ft and 420Kts (p. B9-78)

In the figure above, the solid curve is the one following the law:

- Null lift for AoA angle equal to -4.00 deg. - CL(AoAT) is linear up to 20deg with a value of 0.70 - CL max is equal to 1.04, reached for an AoA of 40

deg.

Other symbols (x), (+), (o) are values extracted from diagram at 20,000ft and 660Kts (p. B9-76), 30,000ft at 540Kts (p B9-77) and 40,000ft and 450Kts (p. B9-78)

In the figure above, the solid curve is the one following the law:

- Null lift for AoA angle equal to -4.50 deg. - CL(AoAT) is linear up to 40deg with a value of 1.04

Other symbols (x), (+), (o) are values extracted from diagram at 20,000ft and 710Kts (p. B9-76), 30,000ft at 590Kts (p B9-77) and 40,000ft and 480Kts (p. B9-78)

-0.3000

-0.2000

-0.1000

0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.0000

1.1000

-10.00 0.00 10.00 20.00 30.00 40.00

CL(AoA) Mach in [1.15;1.25]

-0.4000

-0.3000

-0.2000

-0.1000

0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.0000

1.1000

-10.00 0.00 10.00 20.00 30.00 40.00

CL(AoA) Mach in [1.25;1.35]

-0.3000

-0.2000

-0.1000

0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.0000

1.1000

1.2000

-10.00 0.00 10.00 20.00 30.00 40.00

CL(AoA) Mach in [1.35;1.45]

-0.3000

-0.2000

-0.1000

0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.0000

1.1000

1.2000

1.3000

-10.00 0.00 10.00 20.00 30.00 40.00

CL(AoA) Mach in [1.45;1.55]

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In the figure above, the solid curve is the one following the law:

- Null lift for AoA angle equal to -3.70 deg. - CL(AoAT) is linear up to 40deg with a value of 1.10

Other symbols (o) are values extracted from diagram at 40,000ft and 650Kts (p. B9-78)

AoA limitations Data extracted from “Performance data manual F-4C,D,E-1-1-S” pages B9-78.

CAS Mach Ng CL(Ng) AoA CL

(AoA) Error

200 0.66 1.72 1.0069 40.00 1.0000 0.68%

300 0.78 3.80 1.0074 40.00 1.0000 0.74%

250 0.81 2.55 1.0013 40.00 0.9947 0.67%

300 0.96 3.30 0.9291 35.00 0.9331 -0.44%

350 1.10 4.90 1.0375 40.00 1.0012 3.49%

400 1.25 5.80 0.9592 31.00 0.9678 -0.89%

450 1.42 5.40 0.6958 25.50 0.8242 -18.46%

500 1.57 5.20 0.5437 16.00 0.5446 -0.17%

550 1.71 5.40 0.4744 14.00 0.4758 -0.31%

600 1.86 5.50 0.4117 12.00 0.4093 0.58%

650 2.00 5.55 0.3582 10.50 0.3575 0.19%

Thrust and Drag coefficient versus AoA At sea level, Sustained turn rates:

The sustained turn rates and load factor at M1.0 are limited by structural limits (6.4G), but are very close to the one that would have been given by thrust to drag balance.

Acceleration schedule from M0.5:

At 10,000ft, starting with sustained and load factor:

-0.3000

-0.2000

-0.1000

0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.0000

1.1000

1.2000

-10.00 0.00 10.00 20.00 30.00 40.00

CL(AoA) Mach in [1.95;2.05]

0.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

40.00

45.00

0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0

AoA Max (mach)

0.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

16.00

0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10

Sustained Turn Rate from Table Computed

Alt Mach CAS Tr Ng Tr(Ng) Average

0 0.30 198 6.25 1.60 6.88 6.56 6.58 0.27% 8.00 43.69

0 0.40 264 9.75 2.80 10.80 10.27 10.35 0.74% 8.00 32.77

0 0.50 330 12.10 4.00 12.79 12.45 12.22 -1.84% 8.00 26.22

0 0.60 396 12.80 4.80 12.92 12.86 12.81 -0.37% 8.00 21.85

0 0.70 462 13.30 5.90 13.72 13.51 13.67 1.16% 8.00 18.73

0 0.80 528 13.60 7.00 14.30 13.95 14.15 1.41% 7.54 15.43

0 0.90 594 12.60 6.97 12.66 12.63 12.66 0.25% 6.97 12.66

0 1.00 660 10.60 6.50 10.61 10.60 10.55 -0.49% 6.40 10.44

0 1.10 726 7.50 5.10 7.51 7.50 7.60 1.28% 6.12 9.06

Tr

(NgMax)

Sustained Turn Rate (4xAIM-7 - 38,796lbs- AA2)

Raw from Diagram CleanedComputed Error Ng Limit

0.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00

0.0 5.0 10.0 15.0 20.0

Mach (time) from Table Computed

From Table Computed

Alt Mach CAS Time(min) Time (s) M(time)

0 0.50 330 0.00 0.0 0.50 0.00%

0 0.55 363 0.04 2.4 0.55 0.45%

0 0.60 396 0.08 4.8 0.61 0.90%

0 0.65 429 0.11 6.6 0.65 -0.64%

0 0.70 462 0.15 9.0 0.70 0.21%

0 0.75 495 0.18 10.8 0.74 -0.72%

0 0.80 528 0.22 13.2 0.80 0.41%

0 0.85 561 0.25 15.0 0.85 -0.26%

0 0.90 594 0.28 16.8 0.891 -1.02%

Error

Acceleration level flight (4xAIM-7-40,000lbs-AG2)

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And acceleration schedule from M0.6:

At 20,000ft, only sustained turn rates and load factor:

At 30,000ft, only acceleration schedule from M0.8:

At 35,000ft, starting with sustained load factor and turn rates:

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.00

11.00

12.00

0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40

Sustained Turn Rate from Table Computed

Alt Mach CAS Tr Ng Tr(Ng) Average

10,000 0.30 165 0.00 1.00 0.00 0.00 0.00 8.00 45.28

10,000 0.40 220 6.40 1.80 6.40 6.40 6.45 0.71% 8.00 33.96

10,000 0.50 275 9.00 2.80 8.95 8.98 8.98 0.07% 8.00 27.17

10,000 0.60 331 9.50 3.60 9.87 9.68 9.86 1.80% 8.00 22.64

10,000 0.70 387 10.00 4.30 10.23 10.11 10.29 1.70% 8.00 19.40

10,000 0.80 443 10.50 5.10 10.70 10.60 10.81 1.98% 7.54 15.99

10,000 0.90 499 10.75 5.75 10.77 10.76 10.88 1.16% 6.97 13.12

10,000 1.00 555 10.00 5.90 9.95 9.98 10.14 1.68% 6.40 10.82

10,000 1.10 613 9.00 5.70 8.73 8.87 9.01 1.63% 6.12 9.39

10,000 1.20 671 7.75 5.30 7.42 7.59 7.66 0.99% 6.12 8.61

10,000 1.30 728 6.25 4.80 6.18 6.22 6.16 -0.91% 6.12 7.94

Sustained Turn Rate (4xAIM-7 - 40,925lbs- AA2)

Raw from Diagram CleanedComputed Error Ng Limit

Tr

(NgMax)

0.60

0.70

0.80

0.90

1.00

1.10

1.20

1.30

1.40

0 10 20 30 40 50 60 70 80 90 100 110 120 130

Mach (time) from Table Computed

From Table Computed

Alt Mach CAS Time(min) Time (s) M(time)

10,000 0.60 331 0.0 0.600 0.00%

10,000 0.70 387 4.6 0.690 -1.45%

10,000 0.80 443 9.5 0.789 -1.32%

10,000 0.90 499 14.5 0.897 -0.34%

10,000 1.00 555 20.6 1.008 0.77%

10,000 1.10 613 27.5 1.102 0.15%

10,000 1.20 671 35.8 1.200 -0.04%

10,000 1.25 700 40.0 1.245 -0.43%

10,000 1.30 728 46.0 1.297 -0.23%

10,000 1.35 756 53.0 1.344 -0.42%

10,000 1.40 784 63.2 1.395 -0.39%

Acceleration level flight (4xAIM-7-40,000lbs-AG2)

Error

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70

Sustained Turn Rate from Table Computed

Alt Mach CAS Tr Ng Tr(Ng) Average

20,000 0.30 138 0.00 0.00 0.00 8.00 47.05

20,000 0.40 184 2.75 1.38 4.20 3.47 3.48 0.12% 8.00 35.28

20,000 0.50 230 5.50 1.88 5.64 5.57 5.56 -0.22% 8.00 28.23

20,000 0.60 279 6.50 2.50 6.79 6.65 6.65 0.09% 8.00 23.52

20,000 0.70 328 7.00 3.00 7.19 7.09 7.09 -0.04% 8.00 20.16

20,000 0.80 377 7.50 3.63 7.75 7.62 7.63 0.07% 7.54 16.62

20,000 0.90 426 7.75 4.00 7.65 7.70 7.69 -0.11% 6.97 13.63

20,000 1.00 475 7.50 4.30 7.44 7.47 7.47 -0.02% 6.40 11.24

20,000 1.10 519 7.00 4.40 6.93 6.96 6.96 -0.06% 6.12 9.75

20,000 1.20 563 6.40 4.40 6.35 6.38 6.38 0.07% 6.12 8.94

20,000 1.30 610 5.75 4.30 5.72 5.74 5.74 0.03% 6.12 8.25

20,000 1.40 660 5.25 4.20 5.18 5.22 5.22 0.05% 6.12 7.66

20,000 1.50 710 4.60 3.90 4.47 4.53 4.53 -0.16% 6.12 7.15

20,000 1.60 758 3.50 3.40 3.61 3.56 3.74 6.12 6.71

Sustained Turn Rate (4xAIM-7 - 40,925lbs- AA2)

Raw from Diagram CleanedComputed Error Ng Limit

Tr

(NgMax)

0.80

1.00

1.20

1.40

1.60

1.80

2.00

2.20

0 30 60 90 120 150 180 210 240

Mach (time) from Table Computed

From Table Computed

Alt Mach CAS Time(min) Time (s) M(time)

30,000 0.80 308 0.0 0.80 0.00%

30,000 0.90 349 7.5 0.90 -0.18%

30,000 1.00 390 16.5 0.99 -0.51%

30,000 1.10 424 30.5 1.10 0.38%

30,000 1.20 458 45.1 1.21 1.23%

30,000 1.30 497 55.5 1.31 0.70%

30,000 1.40 541 65.3 1.40 0.31%

30,000 1.50 585 76.5 1.51 0.45%

30,000 1.60 626 88.8 1.61 0.45%

30,000 1.70 667 103.0 1.71 0.42%

30,000 1.80 708 120.3 1.82 0.86%

30,000 1.85 729 128.0 1.85 0.26%

30,000 1.91 753 148.1 1.92 0.66%

Acceleration level flight (4xAIM-7-40,000lbs-AG2)

Error

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The large error values at Mach number above 1.7 are due to the impossibility to find a combination of drag and thrust that give correct acceleration and sustained turn rates. Assuming that this should be due to the low values of sustained load factor (producing large error ratio), I’ve chosen to compute thrust and drag to fit the acceleration schedule with the minimal error.

And then acceleration schedule from M0.9:

At 45,000ft

Sustained load factor and turn rates:

And then acceleration schedule from M1.0:

0.00

1.00

2.00

3.00

4.00

5.00

0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00

Sustained Turn Rate from Table Computed

Alt Mach CAS Tr Ng Tr(Ng) Average

35,000 0.30 99 0.00 0.00 0.00 8.00 50.14

35,000 0.40 132 0.00 0.00 0.00 8.00 37.60

35,000 0.50 165 0.00 1.00 0.00 0.00 0.00 8.00 30.08

35,000 0.60 202 2.40 1.30 2.62 2.51 2.51 -0.07% 8.00 25.07

35,000 0.70 239 3.25 1.50 3.03 3.14 3.13 -0.42% 8.00 21.49

35,000 0.80 276 3.60 1.80 3.55 3.57 3.56 -0.24% 7.54 17.71

35,000 0.90 313 4.00 2.20 4.13 4.06 4.08 0.47% 6.97 14.53

35,000 1.00 350 4.00 2.40 4.14 4.07 4.06 -0.09% 6.40 11.98

35,000 1.10 384 4.00 2.60 4.14 4.07 4.04 -0.64% 6.12 10.40

35,000 1.20 418 4.00 2.75 4.05 4.02 4.02 -0.06% 6.12 9.53

35,000 1.30 453 3.90 2.80 3.81 3.86 3.86 0.11% 6.12 8.80

35,000 1.40 489 3.75 2.90 3.69 3.72 3.72 0.14% 6.12 8.17

35,000 1.50 525 3.50 3.00 3.57 3.54 3.54 0.05% 6.12 7.62

35,000 1.60 564 3.40 3.10 3.48 3.44 3.44 -0.01% 6.12 7.15

35,000 1.70 603 3.25 3.10 3.27 3.26 3.13 -4.02% 6.12 6.73

35,000 1.80 642 3.10 3.10 3.09 3.09 2.98 -3.85% 6.12 6.35

35,000 1.90 681 2.90 3.00 2.82 2.86 2.44 -14.82% 6.12 6.02

35,000 2.00 720 2.50 2.70 2.38 2.44 6.12 5.72

Sustained Turn Rate (4xAIM-7 - 40,925lbs- AA2)

Raw from Diagram CleanedComputed Error Ng Limit

Tr

(NgMax)

0.90

1.10

1.30

1.50

1.70

1.90

2.10

0 30 60 90 120 150 180 210 240

Mach (time) from Table Computed

From Table Computed

Alt Mach CAS Time(min) Time (s) M(time)

35,000 0.90 313 0.0 0.90 0.00%

35,000 1.00 350 12.0 1.00 -0.43%

35,000 1.10 384 24.9 1.09 -1.25%

35,000 1.20 418 40.0 1.20 -0.32%

35,000 1.30 453 54.9 1.31 1.11%

35,000 1.40 489 67.0 1.41 0.63%

35,000 1.50 525 78.5 1.50 -0.21%

35,000 1.60 564 91.0 1.60 -0.22%

35,000 1.70 603 104.8 1.71 0.54%

35,000 1.80 642 120.0 1.83 1.44%

35,000 1.90 681 137.1 1.93 1.51%

35,000 2.00 720 155.0 2.01 0.35%

35,000 2.04 734 170.8 2.06 1.00%

Acceleration level flight (4xAIM-7-40,000lbs-AG2)

Error

0.00

1.00

2.00

3.00

0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00

Sustained Turn Rate from Table Computed

Alt Mach CAS Tr Ng Tr(Ng) Average

45,000 0.80 220 1.00 1.25 1.79 1.39 1.39 -0.06% 7.67 18.11

45,000 0.90 250 1.90 1.38 2.00 1.95 1.94 -0.30% 7.09 14.86

45,000 1.00 280 2.10 1.50 2.13 2.11 2.11 -0.43% 6.51 12.25

45,000 1.10 312 2.10 1.63 2.22 2.16 2.19 1.42% 6.22 10.63

45,000 1.20 344 2.10 1.75 2.28 2.19 2.20 0.34% 6.22 9.74

45,000 1.30 376 2.00 1.81 2.22 2.11 2.11 0.31% 6.22 8.99

45,000 1.40 408 2.00 1.88 2.16 2.08 2.08 0.08% 6.22 8.35

45,000 1.50 440 2.00 2.00 2.20 2.10 2.10 0.16% 6.22 7.80

45,000 1.60 470 2.00 2.00 2.06 2.03 2.03 -0.07% 6.22 7.31

45,000 1.70 500 1.95 2.10 2.07 2.01 2.01 0.04% 6.22 6.88

45,000 1.80 530 1.90 2.10 1.95 1.93 1.93 0.03% 6.22 6.50

45,000 1.90 560 1.80 2.00 1.74 1.77 1.67 -5.70% 6.22 6.15

45,000 2.00 590 1.50 1.88 1.51 1.51 1.50 -0.55% 6.22 5.85

Sustained Turn Rate (4xAIM-7 - 40,925lbs- AA2)

Raw from Diagram CleanedComputed Error Ng Limit

Tr

(NgMax)

1.00

1.20

1.40

1.60

1.80

2.00

0 30 60 90 120 150 180 210 240 270

Mach (time) from Table Computed

From Table Computed

Alt Mach CAS Time(min) Time (s) M(time)

45,000 1.00 280 0.0 1.00 0.00%

45,000 1.10 312 30.0 1.10 0.06%

45,000 1.20 344 59.2 1.21 0.67%

45,000 1.30 376 85.0 1.31 0.64%

45,000 1.40 408 109.5 1.40 0.34%

45,000 1.50 440 134.0 1.51 0.51%

45,000 1.60 470 158.6 1.62 1.56%

45,000 1.70 500 180.0 1.73 2.00%

45,000 1.80 530 200.3

Acceleration level flight (4xAIM-7-40,000lbs-AG2)

Error

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h. F-4E with slats (TO.556 applied)

Null lift Drag coefficient As the available thrust for this version is assumed to be the same as the one for previous block of F-4E, null lift drag coefficient will be re-computed to fit with acceleration schedule (refer to § Thrust and Drag coefficient versus AoA).

It’s clear that the null lift drag of the slated version is much more important than the one without slats. These versions are much slower than previous blocks of the F-4E powered with the same engine (and also climb much slower).

The result is displayed in the following diagram for clean configuration (Drag Index 0):

Lift coefficient versus AoA F-4E after T.O.1F-4E-556 We should be able to see the impact of the slats on the lift, so we expect a higher maximum lift, but also a higher lift at medium AoA.

Data extracted from “T.O. 1F-4E-1 Flight Manual”, version issued 1

st February of 1979, Appendix “A” related to slated

versions, pages A9-86 to A9-89.

At low subsonic conditions (Mach under 0.8), the following graphic:

Leads to a CL definition as:

- Null lift for AoA angle equal to -5.00 deg.

- CL(AoAT) is linear up to 18deg with a value of 0.77 - CL max is equal to 1.18, reached for an AoA of 40

deg.

Around M0.9, we have:

Leading to:

- Null lift for AoA angle equal to -4.50 deg. - CL(AoAT) is linear up to 15deg with a value of 0.75 - CL max is equal to 1.19, reached for an AoA of 40

deg.

Between M1.0 and 1.10, we have:

Leading to:

- Null lift for AoA angle equal to -4.00 deg. - CL(AoAT) is linear up to 20deg with a value of 0.90 - CL max is equal to 1.20, reached for an AoA of 40

deg.

Around M1.2, we have:

0.0200

0.0250

0.0300

0.0350

0.0400

0.0450

0.0500

0.0550

0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00

-0.3000

-0.2000

-0.1000

0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.0000

1.1000

1.2000

1.3000

-10.00 0.00 10.00 20.00 30.00 40.00

CL(AoA) Mach in [0.0;0.8]

CL(AoA)

5,000ft 300Kts M0.492

20,000ft 300Kts M0.643

5,000ft 450Kts M0.738

30,000ft 300Kts M0.779

-0.3000

-0.2000

-0.1000

0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.0000

1.1000

1.2000

1.3000

-10.00 0.00 10.00 20.00 30.00 40.00

CL(AoA) Mach in [0.85;0.95]

CL(AoA)

30,000ft 350Kts M0.900

5,000ft 550Kts M0.902

20,000ft 430Kts M0.908

-0.4000

-0.3000

-0.2000

-0.1000

0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.0000

1.1000

1.2000

1.3000

-10.00 0.00 10.00 20.00 30.00 40.00

CL(AoA) Mach in [1.0;1.1]

CL(AoA)

30,000ft 400Kts M1.030

40,000ft 330Kts M1.045

5,000ft 640Kts M1.049

20,000ft 500Kts M1.056

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Leading to:

- Null lift for AoA angle equal to -3.00 deg. - CL(AoAT) is linear up to 24deg with a value of 0.87 - CL max is equal to 1.10, reached for an AoA of 40

deg.

Around M1.3, we have:

Leading to:

- Null lift for AoA angle equal to -2.50 deg. - CL(AoAT) is linear up to 23deg with a value of 0.73 - CL max is equal to 1.00, reached for an AoA of 40

deg.

Around M1.4, we have:

Leading to:

- Null lift for AoA angle equal to -3.00 deg. - CL(AoAT) is linear up to 23deg with a value of 0.65 - CL max is equal to 1.00, reached for an AoA of 40

deg.

Around M1.5, we have:

Leading to:

- Null lift for AoA angle equal to -3.30 deg. - CL(AoAT) is linear up to 40deg with a maximum

value of 0.96

Around M2.0, we have:

-0.4000

-0.3000

-0.2000

-0.1000

0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.0000

1.1000

1.2000

-10.00 0.00 10.00 20.00 30.00 40.00

CL(AoA) Mach in [1.15;1.25]

CL(AoA)

40,000ft 380Kts M1.193

30,000ft 460Kts M1.206

20,000ft 570Kts M1.215

-0.3000

-0.2000

-0.1000

0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.0000

1.1000

-10.00 0.00 10.00 20.00 30.00 40.00

CL(AoA) Mach in [1.25;1.35]

CL(AoA)

20,000ft 610Kts M1.300

30,000ft 500Kts M1.308

40,000ft 420Kts M1.316

-0.3000

-0.2000

-0.1000

0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.0000

1.1000

-10.00 0.00 10.00 20.00 30.00 40.00

CL(AoA) Mach in [1.35;1.45]

CL(AoA)

30,000ft 540Kts M1.399

20,000ft 660Kts M1.400

40,000ft 450Kts M1.415

-0.3000

-0.2000

-0.1000

0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.0000

1.1000

-10.00 0.00 10.00 20.00 30.00 40.00

CL(AoA) Mach in [1.45;1.55]

CL(AoA)

20,000ft 710Kts M1.500

30,000ft 590Kts M1.512

40,000ft 480Kts M1.514

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Leading to:

- Null lift for AoA angle equal to -3.90 deg. - CL(AoAT) is linear up to 40deg with a maximum

value of 0.95

AoA limitations Data extracted from “T.O. 1F-4E-1 Flight Manual”, version issued 1

st February of 1979, Appendix “A” related to slated

versions, pages A9-86 to A9-89 give the following maximum lift values:

We can see that, at low Mach numbers, there are large values spreading, so we have to smooth values, leading to the following incidence limitations along Mach number:

Thrust and Drag coefficient versus AoA At sea level, we have both sustained turn values:

And acceleration from M0.5:

Same for 10,000ft, starting with sustained turn rates and load factor:

-0.2000

-0.1000

0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.0000

1.1000

-10.00 0.00 10.00 20.00 30.00 40.00

CL(AoA) Mach in [1.95;2.05]

CL(AoA)

40,000ft 650Kts M2.000

Alt CAS Mach Ng CL(Ng) AoA CL(AoA) Error

40,000 200 0.66 2.15 1.2586 40.00 1.1800 6.25%

30,000 300 0.78 3.80 1.0074 40.00 1.1800 -17.13%

40,000 250 0.81 3.15 1.2369 40.00 1.1811 4.52%

40,000 300 0.96 4.25 1.1965 40.00 1.1929 0.31%

40,000 350 1.10 5.60 1.1857 40.00 1.1480 3.18%

40,000 400 1.25 5.75 0.9509 30.00 0.9488 0.22%

40,000 450 1.42 5.50 0.7087 26.00 0.7079 0.11%

40,000 500 1.57 5.50 0.5751 22.50 0.5719 0.55%

40,000 550 1.71 5.55 0.4876 18.50 0.4840 0.74%

40,000 600 1.86 5.70 0.4266 16.00 0.4299 -0.76%

40,000 650 2.00 5.80 0.3743 13.50 0.3765 -0.60%

0.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

40.00

45.00

0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0

AoA Max (mach)

0.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

16.00

0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20

Sustained Turn Rate from Table Computed

Alt Mach CAS Tr Ng Tr(Ng) Average

0 0.30 198 8.25 1.90 8.89 8.57 8.51 -0.69% 8.13 44.44

0 0.40 264 11.50 3.00 11.68 11.59 11.53 -0.51% 8.13 33.33

0 0.50 330 13.05 4.20 13.48 13.26 13.21 -0.43% 8.13 26.67

0 0.60 396 14.00 5.30 14.33 14.16 13.98 -1.27% 8.13 22.22

0 0.70 462 14.50 6.30 14.68 14.59 14.45 -0.98% 8.13 19.05

0 0.80 528 14.50 7.00 14.30 14.40 14.26 -0.96% 7.67 15.70

0 0.90 594 12.00 6.60 11.97 11.99 11.99 0.00% 7.09 12.88

0 1.00 660 8.50 5.40 8.77 8.63 8.49 -1.66% 6.51 10.62

0 1.10 726 1.00 1.20 1.00 1.00 0.98 -2.04% 6.22 9.22

Sustained Turn Rate (4xAIM-7 - 42,777lbs- AA2)

Raw from Diagram CleanedComputed Error Ng Limit

Tr

(NgMax)

0.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00

0.0 5.0 10.0 15.0 20.0

Mach (time) from Table Computed

From Table Computed

Alt Mach CAS Time(min) Time (s) M(time)

0 0.50 330 0.00 0.0 0.500 0.00%

0 0.55 363 0.04 2.4 0.555 0.96%

0 0.60 396 0.08 4.8 0.606 0.96%

0 0.65 429 0.12 7.2 0.654 0.62%

0 0.70 462 0.16 9.6 0.703 0.47%

0 0.75 495 0.20 12.0 0.753 0.40%

0 0.80 528 0.25 15.0 0.814 1.81%

0 0.85 561 0.29 17.4 0.862 1.41%

0 0.90 594 0.33 19.8 0.904 0.44%

Error

Acceleration level flight (4xAIM-7-40,000lbs-AG2)

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Then acceleration from M0.6:

At 20,000ft, we have only turn performances:

At 30,000ft, only acceleration schedule from M0.8:

At 35,000ft, starting with turn performances:

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.00

11.00

12.00

13.00

0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40

Sustained Turn Rate from Table Computed

Alt Mach CAS Tr Ng Tr(Ng) Average

10,000 0.30 165 4.75 1.25 4.28 4.51 4.52 0.05% 8.13 46.06

10,000 0.40 220 7.90 2.10 7.90 7.90 7.89 -0.11% 8.13 34.54

10,000 0.50 275 9.40 2.90 9.32 9.36 9.37 0.07% 8.13 27.63

10,000 0.60 331 10.40 3.80 10.46 10.43 10.45 0.17% 8.13 23.03

10,000 0.70 387 11.00 4.70 11.23 11.11 11.16 0.39% 8.13 19.74

10,000 0.80 443 11.40 5.40 11.35 11.38 11.45 0.63% 7.67 16.27

10,000 0.90 499 10.75 5.80 10.87 10.81 10.77 -0.32% 7.09 13.35

10,000 1.00 555 8.20 4.90 8.21 8.21 8.22 0.15% 6.51 11.01

10,000 1.10 613 6.70 4.40 6.67 6.68 6.59 -1.46% 6.22 9.55

10,000 1.20 671 5.50 3.95 5.45 5.48 5.41 -1.20% 6.22 8.76

10,000 1.30 728 3.75 3.10 3.86 3.81 3.79 -0.51% 6.22 8.08

10,000 1.40 784 0.00 1.00 0.00 0.00 0.00 6.22 7.50

Sustained Turn Rate (4xAIM-7 - 42,777lbs- AA2)

Raw from Diagram CleanedComputed Error Ng Limit

Tr

(NgMax)

0.60

0.70

0.80

0.90

1.00

1.10

1.20

1.30

1.40

0 10 20 30 40 50 60 70 80 90 100 110 120 130

Mach (time) from Table Computed

From Table Computed

Alt Mach CAS Time(min) Time (s) M(time)

10,000 0.60 331 0.0 0.600 0.00%

10,000 0.70 387 5.6 0.697 -0.37%

10,000 0.90 499 17.0 0.904 0.47%

10,000 1.10 613 34.3 1.108 0.73%

10,000 1.20 671 49.0 1.209 0.77%

10,000 1.25 700 59.2 1.261 0.90%

10,000 1.30 728 72.2 1.313 1.03%

10,000 1.325 742 81.3 1.338 0.97%

10,000 1.35 756 94.7 1.360 0.75%

10,000 1.36 762 111.9 1.375 1.09%

Acceleration level flight (4xAIM-7-40,000lbs-AG2)

Error

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70

Sustained Turn Rate from Table Computed

Alt Mach CAS Tr Ng Tr(Ng) Average

20,000 0.40 184 4.25 1.40 4.36 4.30 4.33 0.68% 8.13 35.89

20,000 0.50 230 6.00 1.95 5.95 5.98 6.01 0.47% 8.13 28.71

20,000 0.60 279 7.25 2.60 7.11 7.18 7.20 0.23% 8.13 23.93

20,000 0.70 328 8.00 3.30 7.99 8.00 8.03 0.37% 8.13 20.51

20,000 0.80 377 8.25 3.90 8.38 8.32 8.36 0.58% 7.67 16.91

20,000 0.90 426 8.10 4.20 8.06 8.08 8.07 -0.08% 7.09 13.87

20,000 1.00 475 6.50 3.80 6.52 6.51 6.53 0.30% 6.51 11.44

20,000 1.10 519 5.50 3.60 5.59 5.55 5.57 0.45% 6.22 9.93

20,000 1.20 563 4.90 3.50 4.97 4.94 4.96 0.57% 6.22 9.10

20,000 1.30 610 4.20 3.35 4.37 4.29 4.29 0.14% 6.22 8.40

20,000 1.40 660 3.75 3.05 3.66 3.71 3.65 -1.38% 6.22 7.80

20,000 1.50 710 2.75 2.55 2.78 2.77 2.77 0.26% 6.22 7.28

20,000 1.60 758 0.50 1.00 0.00 0.25 0.00 6.22 6.82

Sustained Turn Rate (4xAIM-7 - 42,777lbs- AA2)

Raw from Diagram CleanedComputed Error Ng Limit

Tr

(NgMax)

0.800

1.000

1.200

1.400

1.600

1.800

2.000

2.200

0 30 60 90 120 150 180 210 240

Mach (time) from Table Computed

From Table Computed

Alt Mach CAS Time(min) Time (s) M(time)

30,000 0.800 308 0.0 0.80 0.00%

30,000 0.900 349 8.4 0.90 0.47%

30,000 1.000 390 16.8 0.99 -0.94%

30,000 1.200 458 47.1 1.20 0.26%

30,000 1.400 541 77.2 1.39 -0.38%

30,000 1.600 626 116.4 1.61 0.37%

30,000 1.700 667 139.1 1.71 0.42%

30,000 1.750 688 153.0 1.76 0.39%

30,000 1.800 708 172.4 1.81 0.42%

Acceleration level flight (4xAIM-7-40,000lbs-AG2)

Error

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Then acceleration schedule from M0.9:

And last at 45,000ft, starting with turn performances:

And Acceleration schedule from M1.0:

0.00

1.00

2.00

3.00

4.00

5.00

0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00

Sustained Turn Rate from Table Computed

Alt Mach CAS Tr Ng Tr(Ng) Average

35,000 0.50 165 0.75 1.00 0.00 0.38 0.00 8.13 30.60

35,000 0.60 202 2.90 1.35 2.87 2.88 2.83 -1.69% 8.13 25.50

35,000 0.70 239 3.75 1.60 3.38 3.57 3.56 -0.08% 8.13 21.86

35,000 0.80 276 4.25 2.05 4.24 4.24 4.26 0.31% 7.67 18.02

35,000 0.90 313 4.25 2.30 4.36 4.31 4.31 0.18% 7.09 14.78

35,000 1.00 350 3.75 2.20 3.71 3.73 3.74 0.14% 6.51 12.19

35,000 1.10 384 3.30 2.20 3.38 3.34 3.34 -0.02% 6.22 10.58

35,000 1.20 418 3.30 2.20 3.10 3.20 3.22 0.78% 6.22 9.70

35,000 1.30 453 3.00 2.30 3.02 3.01 2.99 -0.55% 6.22 8.95

35,000 1.40 489 2.90 2.35 2.88 2.89 2.85 -1.40% 6.22 8.31

35,000 1.50 525 2.75 2.35 2.69 2.72 2.72 0.18% 6.22 7.76

35,000 1.60 564 2.50 2.30 2.45 2.48 2.48 0.04% 6.22 7.27

35,000 1.70 603 2.25 2.20 2.18 2.22 2.22 0.00% 6.22 6.84

35,000 1.80 642 2.00 2.05 1.88 1.94 1.94 0.06% 6.22 6.46

35,000 1.90 681 1.75 1.70 1.37 1.56 1.23 -21.35% 6.22 6.12

35,000 2.00 720 0.25 1.00 0.00 0.13 0.00 6.22 5.82

Sustained Turn Rate (4xAIM-7 - 42,777lbs- AA2)

Raw from Diagram CleanedComputed Error Ng Limit

Tr

(NgMax)

0.90

1.10

1.30

1.50

1.70

1.90

2.10

0 30 60 90 120 150 180 210 240 270 300

Mach (time) from Table Computed

From Table Computed

Alt Mach CAS Time(min) Time (s) M(time)

35,000 0.90 313 0.0 0.90 0.00%

35,000 1.00 350 9.8 0.97 -2.98%

35,000 1.20 418 48.3 1.20 -0.08%

35,000 1.40 489 80.9 1.39 -0.73%

35,000 1.60 564 118.0 1.62 1.11%

35,000 1.70 603 136.5 1.71 0.50%

35,000 1.80 642 158.4 1.80 0.04%

Acceleration level flight (4xAIM-7-40,000lbs-AG2)

Error

0.00

1.00

2.00

3.00

0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00

Sustained Turn Rate from Table Computed

Alt Mach CAS Tr Ng Tr(Ng) Average

45,000 0.70 190 0.60 1.00 0.00 0.30 0.41 8.13 21.97

45,000 0.80 220 1.75 1.25 1.79 1.77 1.80 1.60% 7.67 18.11

45,000 0.90 250 1.90 1.40 2.07 1.99 1.99 0.01% 7.09 14.86

45,000 1.00 280 1.60 1.50 2.13 1.86 1.85 -0.57% 6.51 12.25

45,000 1.10 312 1.90 1.50 1.94 1.92 1.89 -1.28% 6.22 10.63

45,000 1.20 344 1.90 1.40 1.56 1.73 1.70 -1.70% 6.22 9.74

45,000 1.30 376 1.50 1.40 1.44 1.47 1.46 -0.41% 6.22 8.99

45,000 1.40 408 1.45 1.40 1.33 1.39 1.39 -0.08% 6.22 8.35

45,000 1.50 440 1.35 1.50 1.42 1.38 1.38 -0.45% 6.22 7.80

45,000 1.60 470 1.25 1.50 1.33 1.29 1.29 0.15% 6.22 7.31

45,000 1.70 500 1.10 1.45 1.18 1.14 1.14 -0.19% 6.22 6.88

45,000 1.80 530 1.00 1.40 1.04 1.02 1.01 -0.63% 6.22 6.50

45,000 1.90 560 0.50 1.20 0.67 0.58 0.56 -3.27% 6.22 6.15

Sustained Turn Rate (4xAIM-7 - 42,777lbs- AA2)

Raw from Diagram CleanedComputed Error Ng Limit

Tr

(NgMax)

1.00

1.20

1.40

1.60

1.80

2.00

0 60 120 180 240 300 360 420 480 540

Mach (time) from Table Computed

From Table Computed

Alt Mach CAS Time(min) Time (s) M(time)

45,000 1.00 280 0.0 1.00 0.00%

45,000 1.10 312 36.0 1.11 0.67%

45,000 1.30 376 114.0 1.32 1.61%

Acceleration level flight (4xAIM-7-40,000lbs-AG2)

Error

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D. Appendix and Figures.

a. Standard Atmosphere.

h (ft)

A(z) (M=1 ft/s)

rho(z) slug / ft

3

M=1 (m/s TAS)

0 1116.45 0.0023769 340.29

5,000 1097.09 0.0020481 334.39

10,000 1077.39 0.0017553 328.39

15,000 1057.32 0.0014957 322.27

20,000 1036.86 0.0012665 316.03

25,000 1015.98 0.0010652 309.67

30,000 994.67 0.0008894 303.18

35,000 972.9 0.0007366 296.54

40,000 968.08 0.0005851 295.07

45,000 968.08 0.0004601 295.07

50,000 968.08 0.0003618 295.07

55,000 968.08 0.0002846 295.07

60,000 968.08 0.0002238 295.07

65,000 968.08 0.000176 295.07

70,000 968.08 0.0001384 295.07

75,000 968.08 0.0001089 295.07

80,000 968.08 8.554E-05 295.07

85,000 968.08 6.653E-05 295.07

90,000 968.08 5.15E-05 295.07

95,000 968.08 4.011E-05 295.07

100,000 968.08 3.138E-05 295.07

i. Corrected Air Speed (CAS). CAS

(Mach / ft) 0.00 0.50 1.00 1.25 1.50 2.00 3.00

0 0 330 660 825 1000 1325 1975

5,000 0 305 610 760 920 1225 1835

10,000 0 275 555 700 840 1125 1695

15,000 0 250 520 640 775 1025 1525

20,000 0 230 475 585 710 950 1430

25,000 0 205 430 525 640 865 1315

30,000 0 185 390 475 585 790 1200

35,000 0 165 350 435 525 720 1110

40,000 0 145 315 400 475 650 1000

45,000 0 130 280 360 440 590 890

50,000 0 115 250 325 390 535 825

55,000 0 105 220 285 350 475 725

60,000 0 93 195 255 320 425 635

65,000 0 83 174 227 285 386 565

70,000 0 75 157 205 257 342 510

75,000 0 66 139 182 229 304 454

80,000 0 60 126 165 207 274 410

85,000 0 54 114 149 186 248 370

90,000 0 48 101 133 166 221 330

95,000 0 42 89 116 146 194 290

100,000 0 40 83 108 136 181 270

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E. Bibliography All documents mentioned here as url can be found in Acrobat Reader (.pdf) format at http://www.checksix-fr.com/downloads/falcon4/Topolo/zip/Project-21 - Flight Manual F-4C,D,E-1-S , T.O. 1F-4C-1, 15

th August 1973 CHANGE 1, from www.flight-manuals-on-cd.com LTD.

- Performance data manual F-4C,D,E-1-1-S, T.O. 1F-4C-1-1, 15th

July 1969 CHANGE 1 from www.flight-manuals-on-cd.com LTD - Flight Manual F-4E, T.O. 1F-4E– 1

st Feb 1979

- NASA_CR-2144 : Aircraft Handling Qualities Data, by Robert K. Heffley and Wayne F. Jewel, NASA December 1972. - NASA_TN_D-5361 : Analysis of lateral-directional stability characteristics of a twin-jet fighter airplane at high angles of

attack. By Joseph R. Chambers and Ernie L. Anglin, NASA August 1969.

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Table of Contents A. Purpose and scope ...................................................................................................................................................................... 1

B. Data Collection ............................................................................................................................................................................ 1

a. Dimensional Data ................................................................................................................................................................... 1

b. Weight and Balance. .............................................................................................................................................................. 1

Empty Weight ............................................................................................................................................................................. 1

Fuel Weight ................................................................................................................................................................................. 2

Load-out Weight ......................................................................................................................................................................... 2

Gross Weight. .............................................................................................................................................................................. 2

c. Angle of attack (AoA) ............................................................................................................................................................. 2

d. Speed limitations. .................................................................................................................................................................. 2

e. Load Factor limitations. ......................................................................................................................................................... 3

Configuration “A” or Clean ......................................................................................................................................................... 3

Configuration “B” or “C” ............................................................................................................................................................. 3

f. External loads Drag. ............................................................................................................................................................... 3

External load Drag Index. ............................................................................................................................................................ 3

Drag Index impact determination. .............................................................................................................................................. 3

C. Data recognition ......................................................................................................................................................................... 4

Define Thrust and Drag coefficient versus AoA. ......................................................................................................................... 4

AoA limitations ............................................................................................................................................................................ 5

a. F-4D (J79-GE-15) .................................................................................................................................................................... 5

Null lift Drag coefficient .............................................................................................................................................................. 5

Lift coefficient vesurs AoA .......................................................................................................................................................... 5

AoA limitations ............................................................................................................................................................................ 8

Thrust and Drag coefficient versus AoA ...................................................................................................................................... 8

g. F-4E (J79-GE-17) without slats (TO.556 not applied) ........................................................................................................... 12

Null lift Drag coefficient ............................................................................................................................................................ 12

Lift coefficient versus AoA ........................................................................................................................................................ 12

AoA limitations .......................................................................................................................................................................... 14

Thrust and Drag coefficient versus AoA .................................................................................................................................... 14

h. F-4E with slats (TO.556 applied) .......................................................................................................................................... 17

Null lift Drag coefficient ............................................................................................................................................................ 17

Lift coefficient versus AoA F-4E after T.O.1F-4E-556 ................................................................................................................ 17

AoA limitations .......................................................................................................................................................................... 19

Thrust and Drag coefficient versus AoA .................................................................................................................................... 19

D. Appendix and Figures. ............................................................................................................................................................... 22

a. Standard Atmosphere. ......................................................................................................................................................... 22

i. Corrected Air Speed (CAS). .................................................................................................................................................. 22

E. Bibliography .............................................................................................................................................................................. 23