service ceiling & manuevers

8/11/2019 Service Ceiling & Manuevers

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3/9/2013

Service Ceiling & Manuevers



An airplane whose service ceiling is12,000Ft. Climbs 920ft/min at sea level.

How long will it require to climb from sea

level to 8,000ft.(Hrs.) (30%)



Turning Flight

• Now consider situations where the acceleration isnormal to the flight path. The most important ofthese is banked turn as illustrated below.

• A side force, Fr, is generated by banking the aircraft

and tilting the lift vector.• This side force acts as to produce centripetal

acceleration that pulls the aircraft around in an arc ofradius R

L

Fr

WR



Turning Flight (continued)

• Note that since the lift vector is tilted by the bankangle, , to maintain level flight, the lift force mustexceed the weight according to:

• If we define a load factor, n, as the ratio of lift toweight, then by vector math:

• Thus, the centripetal force is related to the loadfactor.

W

Ln

1222

nW W L F r

W L cos

L

W

Fr



R

• From physics, we know that thecentripetal force is calculated by:

• Thus, the turn radius, R, is a function ofthe aircraft velocity and load factor:

• Similarly for the turning rate:

Turning Flight (continued)

R

V m F r

2

12

22

n g

V

F

V m R

r

V

n g

R

V

dt

d 12



Pullup Maneuver

• In a pullup maneuver the aircraftsuddenly experiences an increasein lift above that necessary tosupport the weight.

• This is normally achieved byrotating the craft up to a higherangle-of-attack through use ofthe elevator control surface.

• As a result of the imbalance offorces in the vertical direction, theflight path begins to curveupwards as shown in the sketch.

L

W

R



Pullup Maneuver (continued)

• The centripetal force for this maneuver is now in thevertical plane:

• The radius of curvature of the flight path and thepitch-up rate are similarly given by:

• Note that these relations are equally valid for apushover maneuver - a “pullup” with n < 1.0.

)1( nW W L F r

)1(

22

n g

V

F

V m R

r

V

n g

R

V )1(



Pulldown Maneuver

• The pulldown maneuver is theinverted form of the pullupmaneuver.

• In this case, both lift and weight

are contributing to the pitch rate- as a result, simply rolling anairplane inverted will initiate thismaneuver.

• By convention, we will stillconsider lift and thus load factorpositive as sketched.

L

W

R



Pulldown Maneuver (continued)

• Since the lift and weight are now in the samedirection, the downward acting centripetal forces is:

• And the flight path radius of curvature and pitchdown rate are given by:

• Note that as long as n > -1, R and are positive -for n=-1 the plane is in level flight; for n < -1 theplane begins climbing in a “pushup” maneuver.

)1( nW W L F r

)1(

22

n g

V

F

V m R

r

V

n g

R

V )1(



Maneuver Summary

• A highly maneuverable aircraft is one for which themaneuver radius, R, is small and the turn/pitch rate,, is large.

• To achieve this, all the equations derived so far

indicate that a low velocity and high load factor aredesirable!

• High load factors, of course, require strong structures- but the maximum load factor also depends upon

the CL,max of the aircraft and it’s flight velocity.

• To see how load factor and velocity are inter-related,we use a so-called V-n diagram.



Example: An aircraft performs a level turn at a

speed of 250m/sec and a bank angle of 65deg. Findthe load factor, the radius of turn and the angularrate of turn.

service ceiling & manuevers

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