Aircraft Performance

Question 1

What is the relationship between CL and airspeed?
What conditions do we assume?
How does this relate to AoA?

Answer 1

CL = W/(1/2 ρ v^2 S);
Assuming LEVEL FLIGHT and CONSTANT WEIGHT, a CHANGE in SPEED will mean CL must CHANGE in order to MAINTAIN LEVEL FLIGHT;
Since CL = 2πα where α = AoA in RADIANS, a CHANGE in CL will be caused by a CHANGE in AoA. Therefore a CHANGE in AIRSPEED must be done in conjunction with a CHANGE in AoA to MAINTAIN LEVEL flight

Question 2

How does CL change with airspeed and AoA?

Answer 2

CL DECREASES EXPONENTIALLY with INCREASE in SPEED;

CL INCREASES LINEARLY with INCREASE in AoA

Question 3

What are the horizontal and vertical forces acting on an aircraft?

Answer 3

HORIZONTAL: THRUST (T) = DRAG (D);
VERTICAL: WEIGHT (W) = LIFT (L) + STABILISER LIFT (P)

Question 4

What moments exist on the aircraft?

If these are balanced and there is no net force is there still any moment?

Answer 4

MOMENT: NOSE-DOWN pitch moment = NOSE-UP pitch moment about CoG Lx + Pd =Dy where;
x is HORIZONTAL DISTANCE between CoG and LIFT;
d is HORIZONTAL DISTANCE between CoG and STABILISER LIFT;
y is the VERTICAL DISTANCE between CoG and DRAG;
NO NET FORCE does NOT mean NO MOMENT as the FORCES do NOT act through the SAME POINT

Question 5

What is thrust?
What is power available and power required?
What are the equations for each when required and available?

Answer 5

THRUST: FORCE PRODUCED by an AIRCRAFT;
POWER: RATE of WORK being done;
POWER AVAILABLE: POWER of ENGINE;
POWER REQUIRED: POWER needed to OVERCOME the specific amount of DRAG to ACHIEVE certain SPEED
Pa = Ta x v or THRUST x TAS;
Pr = Tr x v or DRAG x TAS
Tr = D;
Ta = Q(V2 - v)

Question 6

What is the equation for horsepower?

Answer 6

HORSEPOWER = P/745.7 = Tv/325;

T is lbs and v is KNOTS

Question 7

What is the brake horsepower, shaft/propeller horsepower and thrust horsepower?
What is the propeller efficiency?

Answer 7

BHP: ENGINE PRODUCED POWER at CRANKSHAFT or TURBINE SHAFT;
SHP: POWER DELIVERED to the PROPELLER SHAFT;
THP: POWER to PRODUCE THRUST;
n(prop) = THP/SHP

Question 8

What is THP?
What affects it?
How does THP change in a normal aspirated engine and a turbo charged engine?

Answer 8

THP: POWER AVAILABLE;
THROTTLE/SPEED and ALTITUDE;
NORMAL ASPIRATED: Pa DECREASES with ALTITUDE, can only PRODUCE 50% of FULL POWER at SEA LEVEL at 19000ft;
TURBOCHARGED: Pa is able to remain CONSTANT until 19000ft

Question 9

What gives the airspeed limits of a propeller aircraft?

Answer 9

The INTERCEPT between POWER AVAILABLE and POWER REQUIRED

Question 10

What is the thrust available equation?
How is a high thrust available achieved?
What is the propulsion efficiency equation?
What is the difference between propeller efficiency (np) and thrust available in propeller aircraft and jet aircraft?

Answer 10

Ta = Q(V2 - v);
There must be a HIGH Q or LARGE (V2 - v);
np = WORK/ENERGY = 2v/(V2 + v);
PROPELLER: Q is LARGE but (V2 - v) is SMALL so it has relatively HIGH PROPULSION EFFICIENCY;
JET: V2 is VERY HIGH and (V2 - v) is LARGE and CONSTANT so it has HIGH Ta and relatively LOW PROPULSION EFFICIENCY

Question 11

What are the characteristics of power and thrust in a turbojet aircraft?

Answer 11

Pa = Ta x v;
Pa INCREASES with SPEED LINEARLY;
Ta is CONSTANT at a RPM and does NOT CHANGE with SPEED;
Ta DECREASES with INCREASING ALTITUDE;
The INTERCEPT between Ta and Tr gives AIRSPEED LIMIT

Question 12

What other names are given to minimum power?

What about maximum L/D?

Answer 12

MINIMUM POWER: MAX ENDURANCE and MIN SINK;

MAXIMUM L/D: MAX RANGE and MIN DRAG

Question 13

How does altitude affect Pa and Pr?

What effect does this have on airspeed limits?

Answer 13

ENGINE CANNOT produce the SAME POWER when ALTITUDE INCREASES/DENSITY DECREASES which DECREASES POWER AVAILABLE;
As AIR DENSITY DECREASES, PROPELLER THRUST and LIFT DECREASE;
Aircraft must fly at HIGHER TAS to MAINTAIN IAS, since Pr = Tr x v the POWER REQUIRED will INCREASE along the BEST L/D line;
Alternatively if TAS is kept CONSTANT AoA must INCREASE to MAINTAIN LIFT which INCREASES DRAG and Pr as Pr = DRAG x TAS;
It INCREASES MINIMUM SPEED LIMIT and DECREASES MAXIMUM SPEED LIMIT

Question 14

What effect does weight have on Pa and Pr

Answer 14

WEIGHT only AFFECTS Pr;
INCREASE in WEIGHT INCREASES CL;
INCREASE in CL INCREASES CD INDUCED;
INCREASE in CD induced INCREASES CD TOTAL;
INCREASE in CD TOTAL INCREASES TOTAL DRAG;
INCREASE in TOTAL DRAG INCREASES Tr;
INCREASE in Tr INCREASES Pr

Question 15

Draw the vectors for a climbing aircraft?
In a climb what is thrust equal to?
What is lift equal to?

Answer 15

T = D + W x sin(Angle of climb)
L = W x cos(angle of climb)

Question 16

What is the equation for angle of climb?

Where does maximum angle of climb occur?

Answer 16

sin(y) = (T - D)/W = (Tv-Dv)/Wv = (Pa - Pr)/Wv;

When T - D is at MAXIMUM ie: MAXIMUM EXCESS THRUST

Question 17

What is the equation for rate of climb?

Where does maximum rate of climb occur?

Answer 17

Vc = v sin(y) = (Tv - Dv)/W = (Pa - Pr)/W

When there is MAXIMUM EXCESS POWER

Question 18

Is there only 1 maximum angle of climb?

Answer 18

No, it depends of the AIRSPEED, for EVERY AIRSPEED there is a MAXIMUM ANGLE of CLIMB

Question 19

What is the absolute ceiling?

Answer 19

The ALTITUDE where there is NO EXCESS POWER ie POWER REQUIRED = POWER AVAILABLE to MAINTAIN LEVEL FLIGHT;
The aircraft CANNOT ACCELERATE in LEVEL flight therefore there is only 1 POSSIBLE AIRSPEED and RATE of CLIMB is 0

Question 20

What is the service ceiling?

Answer 20

The ALTITUDE for PRACTICAL REASONS the RATE of CLIMB is less that 0.5m/s or for some specified rates ie: 2.5m/s

Question 21

What is the definition of a steady turn?

Answer 21

In LEVEL FLIGHT where VELOCITY and ANGLE of BANK are CONSTANT

Question 22

What is the equation for centripetal acceleration?
What is the equation for centripetal force?
What provides the centripetal force?

Answer 22

Ac = (v^2)/r;
Fc = (mv^2)/r or (wv^2/gr)
HORIZONTAL COMPONENT of LIFT (L x sin(AoB))

Question 23

What is the equation for load factor?

Answer 23

1/cos(AoB)

Question 24

For a given airspeed and radius how is angle of bank calculated?

Answer 24

W = L cos(AoB)
Fc = (mv^2)/r = L sin(AoB) = W/cos(AoB) x sin(AoB) = mg tan(AoB) => tan(AoB) = (v^2)/gr

Question 25

How is CL in the turn calculated?

Answer 25

L = W/cos(AoB) and LF = 1/cos(AoB);
In LEVEL FLIGHT L = W so L(B) = L/cos(AoB) = LF x L;
CL(B) = LF x CL

Question 26

What is the equation for the lift produced immediately before a stall in level flight and in a turn?

Answer 26

L = CL(stall) x 1/2 ρ v^2(stall) S
L(B) = LF(max) x CL(stall) x 1/2 ρ v^2(stall) S

Question 27

What is the stall speed equation?

Answer 27

v/v(stall) = √ LF(max) = √ 1/cos(AoB max)

Question 28

What are the speed limits of a power curve?

Where does vs sit in relation to lower limit intersection?

Answer 28

Higher of Vs or LOWER INTERSECTION of Pa and Pr;
Lowest of Vne or HGIHER INTERSECTION of Pa send Pr;
Vs slightly LOWER TAS than INTERSECTION

Question 29

Where does the L/D max sit on each thrust required and power required graph?

Answer 29

THRUST: Where MINIMUM THURST is REQUIRED;
POWER: Slightly higher VELOCITY than MINIMUM POWER REQUIRED

Question 30

How does each drag change with speed on the total drag curve?
Where is the point of minimum drag?

Answer 30

PARASITE DRAG INCREASES with v^2;
INDUCED DRAG DECREASES with 1/v^2 and is FLATTER with INCREASED v;
Where PARASITE and INDUCED DRAG are EQUAL

Question 31

How does power required change with increasing speed?

Answer 31

Quite FLAT before MINIMUM POWER but INCREASES to v^3 shortly after