A/C Performance Flashcards
What is the relationship between Cl and AoA/airspeed?
If we assume level flight and weight remains constant (and a thin symmetrical aerofoil for lift theory)
Cl= W/(0.5pv^2S)
So a change in speed will change Cl, however as seen in lift theory (Cl=2pi&), Cl is a function of AoA. So AoA is what changes Cl not velocity, as a change in AoA will affect V.
Cl will decrease exponentially with V, but increase linearly with AoA
Draw the forces acting on an a/c and what they must be equal too (to be balanced)
Refer to notes for diagram.
Horizontally: T=D
Vertically: L+P=W (P is tailplane in up direction, so if - value means downforce)
What moments exist on an a/c? If they are balanced (no net force) is there any moment?
Nose pitch down moment (L/W & P)
Nose pitch up moment (T/D)
Therefore in for level flight nose pitch down moment = nose pitch up moment (Lx + Pd = Dy).
However no net force does not mean no moment as the forces do not act through the same point on the a/c
Difference between power and thrust?
Equations for Pa, Pr, Ta & Tr?
Thrust is the force produced by an a/c.
Power is a measure of the rate of work being done
Pa= Ta x v
Pr= Tr x v —> P=W/t & W=Fd so P=Fd/t=Fv and Tr is a Force
Tr = D
Ta=Q(V1-V)
How can horsepower be calculated? What does HP represent?
Power
HP= Power/745.7=Tv/325
Where v is in kt and T in lb
How does parasite drag and induced drag change with airspeed? How does this affect total drag?
Parasite drag will increase with TAS^2.
Induced drag will decrease with 1/TAS^2
Total drag will decrease with and increase in speed below Vmd and increase after Vmd
Where is L/D at a maximum on the total drag graph?
Is minimum Pr=max L/D on a power curve? Does this mean Pr min=Tr min?
1) where D parasite=D induced (minimum drag or best L/D ratio speed)
2) no. Min Pr is at a lower TAS than min drag/best L/D TAS. So it can be assumed min thrust required is not at min power required.
How does power change with v on a power curve?
Relatively flat before min Pr, but increases quickly to v^3 after mon Pr
What are the speed limits of an a/c using a power curve?
Where does Vs lie in relation to the lower limit intersection of Pa/Pr?
Highest of Vs or lower intersection of Pa/Pr (Vmin)
Lowest of Vne or higher Vmax
Vs is usually a slightly lower TAS than Vmin
Difference between brake horse power, propellor/shaft horsepower and thrust horsepower?
What is propellor efficiency?
Engine power produced at the crankshaft or turbine shaft is BHP.
Power delivered at the propellor shaft is called SHP
Power that produces thrust is called THP
Therefore propellor efficiency is THP/SHP
How does Pa change with altitude in a normally aspirated engine vs a turbocharged engine?
What affects Pa?
In a normally aspirated engine, Pa will decrease with altitude (50% at 19000ft).
In a turbocharged engine, Pa is able to be maintained until 19000ft.
Throttle and altitude
What are other names min power goes by?
What about max L/D?
P min: max endurance & min sink
Max L/D: min drag and max range and Vx
How does altitude affect Pa and Pr?
What effect does this have on min/max speeds?
As air density decreases, propellor thrust and lift will decrease.
a/c must fly at a higher TAS to maintain the same IAS and as Pr=TrV, the increased V means increases Pr so Pr moves up along the min drag line.
The reduced air density also means in a normally aspirated engine, the engine is unable to produce the same amount of power as a sea level so Pa decreases.
If TAS remains constant AoA is able to increase, which still increases Pr as L will increase which increases drag and Pr=DTr
What is the effect of weight on Pa/Pr?
Only affects Pr as more weight means more lift which increases drag and as Pr=Dv Pr will increase.
Describe Ta, Tr and Pa for jet engine aircraft
Ta is constant for a given RPM (horizontal line) is not affected by airspeed
Tr is still very similar to Tr for propellors
Pa increases with speed linearly (as Pa=Ta x v, and Ta is constant Pa is proportional to V)
What affects Ta for jet powered a/c?
Increase in altitude will decrease Ta
RPM affects Ta
Propulsion efficiency in propellor vs jet engine aircraft?
Ta=Q(V1-V) —> efficiency is 2V/V1+V
Propulsion efficiency is higher in propellors as change in V is reduced but a large Q, in jets change in V is huge so have a reduced efficiency
Draw the climb diagram.
How do you find the values for T & L?
Lift=Weight & Thrust=Drag in S/L flight
In a climb:
T= D + Rcw = D + WsinAoA
L= Vcw = WcosAoA
What are the equations for AoC & RoC?
What is needed in “excess” to achieve them?
AoC: sinAoA=(T-D)/W OR sinAoA=(Pa-Pr)/Wv
RoC: Vc= VsinAoA OR (Pa-Pr)/W
AoC: excess thrust
RoC: excess power
How does altitude affect AoC/RoC?
How does speed affect AoC/RoC?
Altitude decreases both
Speed will increase rate of climb but will decrease angle of climb.
At a given airspeed there is a max AoC
What is the difference between absolute and service ceilings?
Draw the Pa/Pr for propellor and jet a/c for the two different ceilings
Absolute ceiling is when there is no excess powers as Pa=Pr so a climb is not possible. There is only 1 airspeed at which level flight is possible.
Service ceiling is the altitude for practical reasons where RoC is less than 0.5m/s (or a specified rate such as 2.5m/s for jets).
Refer to notes for drawings
Draw the diagram for descending.
How can L & T be calculated in a descent?
T=D - Fcw = D - WsinAoA
L=Vcw=WcosAoA
Equations for AOD & RoC?
AoD: sin AoA=(T-D)/W OR sin AoA= (Pr-Pa)/Wv
RoD: Vd=VsinAoA Or Vd=(Pr-Pa)/W
If Pr-Pa>0 then there is a power deficit and the Fcw provides the “thrust”
How does AoC and RoC equations change in a glide?
What does glide angle depend on? So if we were to change glide angle when at a constant velocity, how would we do that?
REVIEW
As thrust = 0 the equations change slightly.
AoC: sinAoA= D/W
RoC: tanAoA= 1/(L/D) Which approximates sin if AoA small.
Glide angle depends on L/D ratio
Change the AoA or the amount of drag
What defines a steady turn?
In level flight where v and AoB are constant
Equations:
What centripetal acceleration?
What about centripetal force?
Ac= v^2/r
Fc= mv^2/r = wv^2/gr = LsinAoA
Is the horizontal component of lift
Draw the turning diagram, and label the AoB
Check notes
What is lift and weight equal to in a turn?
W= LcosAoA therefore L= W/cosAoA = mg/cosAoA
What is load factor equal to?
L/W, which is greater than 1 in a turn.
Or 1/cosAoA
How can AoB be calculated if v and radius of turn are known?
TanAoA=v^2/gr
How can lift in the turn be calculated? What about the Cl?
L(bank)= LF x W
= Cl(bank) x 0.5pv^2S
= L/cosAoA
Cl(bank)= LF x Cl
What is the amount of lift produced immediately before a stall?
Level flight and in turn
L(max)= Cl(max or stall) x 0.5pv^2(stall) x S
L(bank) LF(max) x Cl(max) x 0.5pv^2 x S
What is the stall speed equation?
V/Vs= SQRT(LF) and as LF=1/cosAoA V/Vs= SQRT (1/cosAoA)
Random considerations:
- is Pa always the max available?
- what directions does thrust act?
- how does Ta change with airspeed in jets? What about Pa?
No, as due to throttle setting. Max Pa is reduced also due to mechanical inefficiencies.
Thrust acts in the direction parallel to velocity which is parallel to drag.
Ta does not change with speed, Pa increases linearly.
Lots of practice questions in notes to go over
Seriously? Go over them!!
How is radius proportional to airspeed and AoB?
R p V
R p 1/AoB
How does increasing altitude affect turning? (Assuming Cf is constant)
Inc ALT inc radius as Cf=mv^2/r and v will have to increase resulting in increased r which will decreases rate of turn
How does a constant v but inc AoB affect turn radius and rate of turn?
Inc rate of turn but decrease radius
