Heavy Lifting RC Electric Airplane DesignW. B. Garner 2017

Introduction and PurposeEvery year the Society of Automotive Engineers International (SAE) sponsors a competition among college engineering students to design, build and fly a heavy lifting RC model airplane. The objective is to develop a plane that can carry cargo subject to a number of design limitations. Cargo consists of passengers (tennis balls) and luggage (bags of sand), with a complicated formula to determine the winners, at least for the flight part. The objective is to maximize the passenger/luggage combination carried.

Here are the primary design limits1.Maximum weight of 50 poundsElectric motor, maximum 1000 Watts into the controller, automatic limiter requiredMaximum voltage 25 VoltsTake off in no more than 200 feetMake one complete field circuit – takeoff, climb, fly the pattern, land in less than 400 feet.Must fly empty with no mods allowed for absence of cargo or passengersSand as luggage (no lead)

The original intent of this project was to design, build and fly such a plane. However, the planes that emerge from these competitions are very large and really require teams of people to accomplish. At maximum weight the power loading is only 20 Watts per pound, well below normal model practice. Each phase of flight poses design challenges that affect the overall design.

A preliminary design was started for a 25 pound, 500 Watt set of limits, but it soon became obvious that a very large plane was still required. It was decided to design a scaled down version with simplified cargo objectives. The adopted limits are as follows.

Maximum weight 10 poundsElectric power, 200 Watts maximum, auto limited (20W/lb at 10 lbs)Takeoff in no more than 200 feetLand in 400 feetMaximize total cargo – no passengersAny material other than lead for cargoFly the same circuit

Flight FundamentalsBefore beginning the design description it is worthwhile to review the fundamentals of flight. The general form of the steady state flight equations occur in climbing (or descending) flight. Level flight is a specific form of this condition. The picture shows the geometry and force relationships.

1 This document uses the foot-pound-second system of measurement. To convert to metric:1 ft/sec = .308 m/sec: 1 pound = .4536 Kg: 1 pound force (lbf) = 4.45 Newtons

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The resulting equilibrium forces are given by the following equations.

L = W*cos (Ɵ)

T = D + W* sin (Ɵ)

Where:

L is lift, lbfW is weight, lbT is thrust, lbfƟ is the angle between horizontal and the velocity vector, V, ft/secV is the air speed, ft/sec

The associated rate of climb, ROC, is given by:

ROC = (T*V – D*V)/W, ft/sec

And the angle of climb, AOC, is given by:

AOC=arcsine (ROC/V), radians

The rate of climb or descent is zero when T =D, positive when T > D and negative when T < D. The ROC is inversely proportional to the weight, so an increase in weight results in a decrease in climb rate. ROC increases with a decrease in weight.

T*V and D*V are power values in ft-lbf/sec. T decreases with V and D increases with V; the amount depends on the power system characteristics for T and the plane characteristics for D.

T*V is the propeller exhaust power producing thrust. It is some fraction, E, of the available power, Pin, into the motor-propeller combination. E is the efficiency of the combination at a particular operating

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point & can vary. However, there is an upper limit to E because of the inherent inefficiencies of motors and propellers. A good quality RC motor will have an efficiency of about 85%. Propeller efficiency varies widely, depending on size, pitch, air speed and revolution rate. The best efficiency is around 70% when the prop is operating at its “sweet spot” ratio of V/(n*Dm), where n is the revolution rate and Dm is the propeller diameter. Therefore the maximum value for E is about 0.7*0.85 = 0.6 and is generally less.

Therefore the maximum value of T*V is about 0.6*Pin. Pin is 200 Watts. To convert ft-lbf/sec to Watts, divide by 1.36.

T*V = 0.6*Pin/1.36 = 0.44 *Pin, ft-lbf/sec

Since Pin = 200 Watts, T*V = .44*200 = 88.2 ft-lb/sec maximum

Or the maximum thrust power is Pthrust = .6*200 = 120 Watts.

Another measure is the ratio of thrust power to weight or 120/20 = 6 W/lb, a very low value.

What does this all mean? It means that the design is severely thrust limited.

Thrust for any propeller deceases with air speed; the rate depends upon the pitch to diameter ratio. The higher the ratio is the lower the rate of decrease. The trade is that the higher ratio will produce less thrust at low air speeds for a given input power limit.

It is desirable to have high thrust on takeoff to accelerate within the distance limits. It is desirable to have high thrust at higher speeds to facilitate maneuvering such as climbs or turns. Hence there is a trade between the two modes of operation.

In any either case it is desirable to reduce the drag to as low a value as possible.

The Equation for drag is as follows:

Drag = wing parasitic drag + wing induced drag + fuselage drag + tail drag

Cdp = Cdwing +Cdfus*Sf/Sw + CDtail*St/Sw.

Cd wing is the wing parasitic (profile) drag coefficient, varies with angle of attack

CDfus is the fuselage drag coefficient, S f is the fuselage maximum cross section area, Sw is the wing area.

Cdtail is the tail drag coefficient; St is the area of the two stabilizers.

Dinduced = 0.318*W*K*rho/ (V*2*B^2)

Drag = Cdp*0.5*rho*V^2*Sw + Dinduced

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Where:

Cdp is a drag coefficient that includes both wing and fuselage parasiticRho is air density, slugs/ft^3S is the area subject to the drag, ft^2K is factor that accounts for wing shape, ranging from about 1 to about 1.05B is the wing span, ft

Decreasing wing area decreases parasitic drag but it also increases stall speed, requiring higher takeoff speeds and higher operating speeds. But higher speeds create greater drag due to the V^2 variable.

Induced drag is reduced by increasing wing span (B). It decreases with increasing air speed as the wing moves from a large angle of attack to a smaller one.

This graph illustrates the variation of drag with airspeed assuming the plane is operating above stall speed.

Stall conditions occur where the curves end at the left. The drag in this region is controlled by the induced drag. As the velocity increases the drag decreases until a minimum is reached. Then the drag increases as the parasitic drag, proportional to V^2, takes over. At about 70 ft/sec the drag and thrust are equal. The plane is in level flight equilibrium but cannot climb. Climb can occur only when the thrust exceeds the drag. In this case that region is approximately 40 to 70 ft/sec.

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The next graph plots the ROC and AOC for a 12x10 propeller for the previous conditions.

The best rate of climb is about 140 feet per minute and occurs at V around 40 ft/sec. The best angle of climb occurs just above stall, around 38 ft/sec. The other notable fact is that the climb angle is very shallow and has implications for actually flying the airplane.

Design OverviewThere is no practical way to go directly to a ‘final’ design as there are too many variables and values to choose from. It is necessary to do iterative selection and analysis to arrive at a suitable design. The approach taken was to examine each stage of flight, determine which was the most challenging and use it for a starting point.

Take-offThis stage is the second most challenging because the plane must be accelerated to takeoff speed in a limited distance subject to power system & drag limitations. What makes it complicated can be observed from the take-off velocity, acceleration, roll velocity and distance equations.

Vlo = 2∗Wrho∗S∗Clo , take-off velocity, ft/sec

Drag=Cd*rho*Vroll^2*S, lbf

Lift = .5*rho*V^2*S*Clroll, lbf

Vroll = a*t, ft/sec

Distance = a*t^2, feet

a =g∗¿¿, acceleration, ft/sec^2

t is time, secondsg is gravitational constant, 32.2 ft/sec^2

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rho is air density, slugs/ft^3Clo is lift coefficient when rotated to lift offClroll is lift coefficient during rollCd is wing total plane drag coefficient during rollS is wing areaW is weight, lbsT is Thrust, lbfDrag is the total drag of the plane, lbf, a function of VCf is rolling coefficient of frictionL is wing lift, lbf, a function of V

While g, W and Cf are constant, Thrust, Drag and Lift are functions of velocity, V. Thrust decreases as V increases, while Drag and Lift increase. Hence to get a good analytic result it is necessary to develop relationships for the variable parameters as a function of velocity. But thrust is a function of the propeller- motor –input power combination while lift and drag are primarily a function of wing and fuselage design (wing area, span, airfoil; fuselage size, area & shape).

Climb OutThe most challenging part of the design is climb out after liftoff. Once rotated to lift off, the plane must gain altitude to cruising altitude and speed. The friction component of the drag is zero, but now the lift must increase enough to overcome the load caused by the additional component of weight acting against gravity. In this case the plane must accelerate more to equilibrium. However, as speed increases the thrust decreases while the drag increases. The key to this dilemma lies in careful propeller diameter and pitch selection and drag reduction.

CruiseIf the plane can take-off and climb to altitude it can cruise as well.

LandingIn landing the plane must descend at above stall speed. The thrust goes to zero so braking is generated by drag and wheel friction. Both of these values are relatively small compared to the planes momentum so roll outs can be long. Some form of braking, such as flaps or spoilers, may be needed.

Climb Design & AnalysisA major limitation for climb and take-off is the very low power available to the motor and propeller. Therefore a series of assumptions based on experience will be made about the power system in an attempt to reduce the number of possibilities to a practical set of motor and propeller selections.

Power LimiterThe power limiter can be used to advantage in selecting power system components. It measures the supply current and voltage to the input of the ESC. It takes as input the control signal from the receiver and delivers a modified version to the ESC. If the input power begins to exceed the allowed value, the limiter changes the throttle signal to the ESC to reduce the average voltage applied to the motor. If the input power is less than the allowed value the limiter increases the throttle value to the ESC, increasing

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the motor applied voltage. If the throttle setting from the receiver results in a lower than maximum power demand the limiter leaves the receiver throttle setting unchanged and passes it on to the ESC.

This feature is useful from a design viewpoint. As current is drawn from a battery the voltage begins to decrease and the maximum value of voltage that can be applied to the motor decreases. At full throttle, such as during take-off or climb, this decrease in voltage results in a decrease in motor rpm and a reduction in propeller thrust. As long as the input voltage to the limiter is higher than that required of the motor, the motor voltage will adapt, maximizing the thrust available. So the choice of battery voltage and motor Kv can be adjusted to advantage.

Propeller – Motor TradesThere are a very large number of possible propeller plus motor combinations that might work. Some characteristics of typical motors and propellers will be used in conjunction with propeller equations to generate a list of candidates.

Motor efficiency is fairly constant over a wide range of current draw conditions. A high efficiency motor with an efficiency of 85% will be assumed. Given the 200 W input limits, the power available to the propeller is then 0.85 * 200 = 170 W.

Propeller thrust is given by the following equation.

T = Ct*Rho*N^2*Dm^4, lbf

Propeller input power is given by the following equation.

Pp = Cp*Rho*N^3*Dm^5*1.356, Watts

Rho is air density, slugs/ft^3N is the shaft revolution rate, rev/secDm is the propeller diameter, feet

N = Vm*Kv/60

Vm is the voltage applied to the motor (not the source voltage)Kv is the motor constant, rpm/Volt

The next step is to make some choices for Ct, Cp, and V, then try values for D as a variable to generate estimates for Kv.

The key propeller selection characteristic is the ratio of pitch to diameter. Low ratio props (0.4 to 0.5) produce the greatest torque (thrust) at low air speeds but decrease rapidly as the air speed increases. While they might work for take-off, they may not produce enough thrust for climb or sustained flight. On the other hand, high pitch/diameter ratios (>0.8) have the lowest low airspeed thrust but provide sustained thrust at high air speeds. Since both high and low speed requirements exist, a compromise is

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necessary. The compromise is to select an initial pitch/diameter ratio of 0.7 and then modify the choice based on analysis.

The next step is to select values for Ct and Cp. The values of these coefficients decrease with air speed for a constant rpm, our case. Therefore values are selected representative of a moderate air speed to rpm ratio. The selections are Ct = 0.1 and Cp = .05, typical of a pitch/diameter ratio of 0.7.

The next step is to select a battery voltage and a motor voltage. For this purpose the battery voltage selected is 11Volts (3S Lipo battery) and the motor voltage is 7 volts. This latter selection will be discussed later.

To summarize the selections:

Vbattery = 11 voltsVmotor = 7 VoltsCt = 1.0Cp =0.05Rho = .001927 (standard value at 6,800 feet altitude, the author’s home field value)Pp = 170 Watts

From the equation for prop power:

Kv =3√ Pp∗0.737∗602

Cp∗rho∗D5∗Vmotor , rpm

Inserting the values by selecting the diameter in inches and then putting the diameter and Kv into the thrust equation:

Vmotor = 7 Volts

pitch, in 6.3 7 7.7 8.4 9.1 9.8D, in 9 10 11 12 13 14D, ft 0.75 0.83 0.92 1.00 1.08 1.17Kv 1511 1268 1082 936 819 724T 1.90 2.03 2.17 2.30 2.42 2.54rpm 10579 8876 7572 6550 5732 5066

Rpm =Vmotor*Kv

This next table repeats the calculations for a Vmotor of 10 Volts. Comparing the tables, increasing the voltage causes the Kv to decrease. The lower the Kv is generally the heavier the motor since weight in such a small plane is critical. Also the choice of motors tends to be limited.

Vmotor = 10 Volts

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pitch, in 6.3 7 7.7 8.4 9.1 9.8D, in 9 10 11 12 13 14D, ft 0.75 0.83 0.92 1.00 1.08 1.17Kv 1058 888 757 655 573 507T 1.90 2.03 2.17 2.30 2.42 2.54rpm 10579 8876 7572 6550 5732 5066

The next step is to select one of the diameters and do a detailed analysis using the actual Ct and Cp for that propeller. The motor characteristics also need to be included.

The objective of this exercise is to choose a prop with the ‘best’ thrust characteristics. The other deciding factor is the pitch selection as it comes in discrete values. The choice, somewhat arbitrary, is a 12 x8 size. The corresponding Kv is about 940, T about 2.3 lbf and rpm about 6550. There are a number of motors available near this Kv value with sufficient power capability to do the job.

A representative motor is the Turnigy G15 Brushless Outrunner 950 Kv.

Battery: 3 to 4 cellsKv: 950Imax: 34 AmpsNo load current: 2.0A/10VResistance: 0.03 OhmsWeight: 152 Grams

Thrust as a Function of Air SpeedCalculating the thrust as a function of air speed for a motor is complicated and beyond explaining for this document. The author has a computer program to do so and the results are shown here. The effect of the limiter on holding the input power constant is included. The following graph illustrates the effect of propeller size and pitch on thrust as a function of air speed.

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Wing and Air Foil SelectionThe next step is to choose initial plane parameters, principally the wing size and air foil type.

The general equation points to minimizing the drag as a function of air speed. It is also necessary to have sufficient lift coefficient to keep the stall speed such that takeoff can occur within the distance limit. Airfoils with high maximum Cl have the lowest stall speed but also have relatively high parasitic drag coefficients. Airfoils with low maximum Cl tend to have relatively low drag coefficients but have higher stall speeds. The selection is therefore a compromise with the selection toward climbing flight favored.

There are literally hundreds of air foils to choose from. Many are designed for a specific purpose that does not match the present requirements. Two representative air foil polar coordinates are shown in the next graph. The S2091 has much lower drag coefficients over its primary Cl operating range from 0 to 1 than does the S1223 airfoil. The S1223 airfoil operates over a much wider range of lift coefficients but at higher drag. The S1223 airfoil is highly cambered with a concave under surface that tapers to a very thin trailing edge. It also does not lend itself to flaps. The S2091 is mildly cambered and straight forward to make. It will support flaps.

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The next graph plots the drag for the air foils as a function of air speed. The S1209 has lower drag over a wider range of air speed than does the S1223. It is therefore a better choice for climb and maneuvering flight. It does have a higher stall threshold so may require greater takeoff distance to get airborne.

The values for wing area and span were selected after several runs of the model. A larger area would decrease stall speed but increase drag. Decreasing area will increase stall speed but reduce drag somewhat. The final value will require more extensive analysis.

The wing span was made as long as deemed reasonable to construct as that reduces the induced drag at near stall where the greatest climb rate is obtained.

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Climb Analysis ResultsMultiple combinations of airfoil and propeller size where examined and the ‘final’ results are shown in this graph. The curves are identified first by propeller size, either 12x12, 12x10 or 14x12 then by airfoil type, either S2091 or S1223.

The maximum rate of climb is the greatest for the S2091 air foil as it produces less drag than the S1223 air foil. The prop size makes little difference in the results with the 14x12 producing the ‘best’ results. It so happens that the propeller thrusts are essentially the same in this range of air speeds. The S1223 has a lower stall speed than does the S2901 airfoil as indicated by the relative locations of the sets of curves along the V axis.

The climb angle equation is given by:

AOC = arcsine (ROC/V)*57.2 degrees

Assuming the peak ROC to be 140 ft/minute and V = 42 ft/sec and adjusting for time differences,

AOC = 3.2 degrees; an extremely shallow angle. This means that in order to climb the plane must be flown at a small angle near stall and will take considerable distance to gain altitude. It also means that turns must be made at very shallow angles to avoid stall.

Maximum cruise speed occurs when the rate of climb becomes zero, or about 55 ft/sec (37 mph).

In summary the S2901 airfoil is preferred and either propeller is OK. Ground and flight tests can be used to make a final selection.

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Drag CompositionThe analyses made a number of assumptions in order to estimate the total drag. The next graph shows how the drag components vary with air speed.

There are three drag components illustrated. The profile drag is the parasitic drag due to the wing. It is the smallest of the drag contributors below about V = 50 ft/sec. The value of its drag coefficient was taken from the previous plot comparing S1223 and S2901 Cd vs Cl. The change in Cl with change in V is included in the results.

The induced drag decreases with V, being the largest contributor at the low end of the V range, and then decreasing to nearly negligible value at the high end.

The parasite drag is due to the drag of the fuselage and tail surfaces. It becomes dominate at the higher end of the speed range. This result is due to the choice of drag coefficients selected and estimates of the effective drag areas of the fuselage and tail surfaces. It was assumed that the fuselage was of a rectangular cross section, moderately shaped from front to rear and that it sported fixed wire landing gear with standard tires. The tail airfoils were assumed to be flat surfaces with hinged control surfaces.

Unlike wings, there is little information available to aid in estimating the drag of fuselages as they vary greatly with the type and construction used.

The drag can be reduced considerably from that presented here by careful design and construction. Here are some methods of reducing the drag to a minimum.

-Look at sail planes as a guide as they are designed specifically to minimize drag.

-Minimize total surface area.

-Make the cross section circular along the entire fuselage length and as small as possible.

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-Taper the fuselage length smoothly from front to rear.

- Employ carbon fiber tail booms to reduce total surface area.

- Enclose the motor in a cowling or place inside the fuselage and use a spinner.

-Use true air foils for the tail surfaces & consider going to an all-moving horizontal stabilizer.

- Mount the horizontal stabilizer high on the vertical stabilizer. (Minimizes wing shadowing & allows smaller surface area. It also minimizes prop wash effects.)

- Enclose the landing gear in fairings and the wheels in pants.

- Consider placing the wing on a pylon to reduce wing- fuselage drag interaction.

Doing these things could reduce the drag by at least half.

The effects of prop wash are not included. It can be minimized by making the ratio of prop swept area to fuselage cross-sectional area as great as possible. About 80% of the accelerated air flow from a propeller occurs from about 50% of the radius outward and virtually all of it occurs beyond 25% of the radius. Its velocity also decreases as the swept area increases. Hence making the ratio as great as possible minimizes prop wash drag.

As the flow moves backwards, it contracts with distance, eventually becoming as one with the undisturbed air conditions. Reducing the fuselage area with distance tends to counter this contraction effect.

Takeoff AnalysisThe analysis for takeoff assumes the S2901 airfoil and compares the results for propeller sizes 0f 21x10, 12x12 and 14x12. No head wind is assumed. The defining equations are as follows.

Vlo = 2∗Wrho∗S∗Clo , take-off velocity, ft/sec

Drag=Cd*rho*Vroll^2*S, lbf

Lift = .5*rho*V^2*S*Clroll, lbf

Vroll = a*t, ft/sec

Distance = a*t^2, feet

a =g∗¿¿, acceleration, ft/sec^2

T, D and L are all functions of speed, V. There is no closed form solution so an numerical method was employed. The Table illustrates the method. Time is divided into small equal increments. To start, the initial acceleration, a, is calculated for D & Cf equal to zero and the thrust T calculated for that condition.

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t, sec dv, ft/sec

v, ft/sec

drag, lbf

lift, lbf T, lbf a, ft/sec^2

dd, ft d,ft 1208

0 0 0 0 0 2.11 5.83 0 00.6 3.50 3.50 0.00 0.06 2.11 5.82 2.10 2.101.2 3.49 6.99 0.01 0.23 2.10 5.79 4.19 6.291.8 3.47 10.46 0.03 0.51 2.09 5.73 6.28 12.572.4 3.44 13.90 0.04 0.89 2.07 5.64 8.34 20.913 3.38 17.28 0.07 1.38 2.05 5.53 10.37 31.283.6 3.32 20.60 0.10 1.96 2.02 5.41 12.36 43.644.2 3.24 23.85 0.13 2.63 1.99 5.26 14.31 57.944.8 3.16 27.00 0.17 3.37 1.95 5.11 16.20 74.155.4 3.07 30.07 0.21 4.18 1.92 4.94 18.04 92.196 2.97 33.04 0.25 5.05 1.88 4.77 19.82 112.016.6 2.86 35.90 0.30 5.96 1.84 4.59 21.54 133.557.2 2.75 38.65 0.35 6.91 1.81 4.40 23.19 156.747.8 2.64 41.29 0.40 7.89 1.77 4.22 24.77 181.518.4 2.53 43.82 0.44 8.88 1.73 4.03 26.29 207.819 2.42 46.24 0.50 9.89 1.69 3.85 27.75 235.559.6 2.31 48.55 0.55 10.90 1.66 3.67 29.13 264.6810.2 2.20 50.75 0.60 11.91 1.62 3.49 30.45 295.1310.8 2.09 52.85 0.65 12.92 1.59 3.32 31.71 326.8411.4 1.99 54.83 0.70 13.91 1.56 3.15 32.90 359.74

At the end of the interval, the change in velocity, dv, is calculated using the previous value of acceleration, a, and the cumulative increase in V is calculated. Using this value of V, the drag and Thrust are calculated as is the change in distance for the interval. The cumulative distance is then calculated. This process is repeated until termination.

The next graph is a plot of takeoff distance as a function of speed, V, for three propeller sizes. The required minimum takeoff speed is 39 ft/sec. The results indicate that taking off under these conditions is marginal at best. The 14x12 prop does slightly better than the others so would be first choice.

It was also assumed that the field altitude is 6,800 feet where the air density is about 80% of sea level. If the field were at sea level the takeoff distance would be somewhat shorter and climb performance better.

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The following conditions were assumed.

Sw = 6 ft^2B = 9 ftClroll = 0.8, A fixed value that maximizes lift while limiting Cdwing.Cl_off = 1.14, 80% of stall ClCf = 0.03, friction coefficient, a guessCdp = .025, combined parasitic estimate

The presence of a modest head wind reduces the required lift off speed in proportion, so this combination might work with a head wind. Head winds do not affect performance once the wheels leave the ground.

LandingMinimum landing distances are achieved by a combination of good aircraft design and good piloting skills. The objective in a good landing is to have the aircraft at minimum controllable speed and attitude up the point of touch down; then land just at stall where the air speed is least and the plane will remain on the ground.

At touch down the thrust should go to zero and the plane is decelerated by the frictional and aircraft surface drag. The aircraft as described to this point has been designed for minimum drag and high lift at maximum thrust. These forces are low so roll out will be long. The next figure illustrates this result assuming there is no additional drag producing forces.

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This best case condition indicates that the plane will roll well beyond the 200 foot limit.

Drag Additions.There are a number of ways to add deployable drag inducing devices. These include flaps, for which there are several kinds, spoilers, airbrakes, deployable parachutes and wheel brakes. Of these the simplest is the plane flap, a hinged section of the trailing edge that deflects downward. It increases the maximum lift coefficient while adding substantial additional drag when fully deployed. It is beyond the scope of this document to evaluate, select and design a suitable flap. Rather, the requirements for the required minimum additional drag will be estimated and the design to meet that requirement deferred.

It will be assumed that the approach speed at touchdown is 25% higher than stall and the value of wing Cdo increased until the roll distance limit is met. It will also be assumed that the flaps will increase the maximum Cl from 1.4 to 1.7, taking into account that the flaps do not typically span the full wing span.

The approach speed is 40 ft/sec and the minimum composite Cdo is estimated at 0.09.

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SummaryThese are the characteristics of the initial design and the resulting performance estimates.

Propeller: 14x12 Thin electricMotor: Turnigy G15

Kv = 950Rm = .03 OhmsIo = 2 A @ 10 VMax Current 34 AmpsWeight 5.36 Oz (152 grams)

Battery: 3S LiP0 (11.1V)Power Limiter: 200 Watts

Wing: 6 ft^2 by 9 ft spanAirfoil S2091Cl maximum 1.4

Weight: 10 lbs maximumStall airspeed: 39 ft/secTakeoff Distance: Marginally 200 feet @ 6,800 ft elevationMaximum Rate of Climb: 140 ft/minute at 42 ft/secMaximum Angle of Climb: 3 degrees at about 40 ft/secLanding Distance: <400 ft with flaps & Cdo drag coefficient > 0.09

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Sea Level PerformanceThe results presented to this point assumed that the elevation was 6,800 feet. The lower air density has a marked effect on performance. The following graphs show what would happen if the model were operated near sea level.

Stall speed is lowered, lift and drag increase as does thrust. The net effect is a significant shortening of takeoff distance.

The Rate of Climb and Angle of Climb increase as does the range of speeds where they are positive.

A case can be made for equalizing the power limits to compensate for differences in air density with altitude. In that case the power limit should be scaled inversely proportional to air density relative to sea level. For the case of 6,800 feet this ratio would be .002376/.001927 = 1.23, or the power permitted

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would be 1.23*200 = 246 Watts. The thrust will increase, reducing takeoff distance and increasing the rate of climb as illustrated in the next graph.

ReferencesH. C. “Skip” Smith, “The Illustrated Guide to Aerodynamics”, Tab Books part of McGraw Hill, 1992

This book is intended to explain aerodynamics to private pilots. It contains good descriptions of most of aspects of airplane design that are of interest to its audience. It is a good initial book to read prior to going into more detailed design descriptions.

Lennon, Andy, “R/C Model Aircraft Design”, Air Age, Inc., 1996This is the most complete guide available for detailed design of R/C model aircraft. It covers all

aspects of aerodynamics as applied to models as well as some construction suggestions.

Simmons, Martin, “Model Aircraft Dynamics”, Special Interest Model Books, UK, Fourth Edition, 2002This book is excellent for descriptions of aerodynamics as applied to models, primarily sail

planes. It tends to be light on analytics although there are appendices that address some key aerodynamic issues. There are also lists for some airfoils with wind tunnel test results.

Abbott & Doenhoff, “Theory of Wing Sections”, Dover Publications, New York, 1959This book is devoted to the theory and testing of wing airfoils. In the present context it has some

data on the performance of different types of flaps. It is highly theoretical and difficult to follow without a good understanding of aerodynamics.

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