Chapter 8
Prop Aircraft Basic Performance
The basics:
In turbojet aircraft the engine produces thrust directly.
In prop aircraft, the powerplant does not produce thrust directly.
The engine produces power which turns the prop.
The prop is what produces the thrust.
So What about The Fuel Question
Fuel consumption is related to power not thrust.
So power becomes the determining factor in endurance and range.
Review of Terms
A force may be considered to be pressure, tension, or weight and is usually expressed in pounds.
Work is when you use a force to move something
so force x dis = work
Horse Power
For example you have an airplane which needs to be pulled up to the gas pumps 100 feet away, lets say on level ground and the plane weighs 2200 lbs..
If you attached a scale to the plane and found it took 55 lbs. of force once you got it rolling, 55 x 100 would result in 5500 ft-lbs. of work was done to get the plane to the gas pumps.
Horse Power
The amount of work has nothing to do with time. It could take all week or a hour and still only 5500ft-lbs. of work is done.
However Power is defined as a time rate of work.
If you pulled the plane to the gas pumps in 1 second, you would be exerting 5500 ft-lb./sec.
Horse Power
Lets say it took 10 sec to do the job. The power would be work/time or 5500/10 = 550 ft-lb/sec.
The most common measure of power is horsepower which happens to be a power of 550 ft-lbs/sec.
So in the example, you would have to exert 1 hp for 10 sec to do the job.
Power Required Curve
The Thrust required curve or drag curve must be converted into power required using this formula:
Induced drag varies inversely as V squared
Induced power varies inversely of the V ratio
Parasite drag varies directly as V squared
Ppower varies directly as the V ratio is cubed
The Power, Thrust, Velocity Thing
The power required for flight depends on the thrust required and flight velocity.
The formula that relates power required to thrust required to velocity is:
Remember, the drag curve is really a thrust required curve
The Power, Thrust, Velocity Thing
So by this equation it takes 1 hp to offset 1 lb of drag at 325kts
at 650kts it takes 2 hp to offset 1 lb of drag
at 162.5 kts it takes 1/2 hp to offset 1 lb of drag
Power Required Curve
Total power required is Ipower + Ppower
The power required curve is flatter in the low speed region than the T required but steeper in the high speed region.
The intersection of the Ppower and Ipower curves is the L/Dmax
The intersection of the Ppower and Ipower curves is the L/Dmax
Power Required Curve
However the min power required is usually in a different place (bottom of the curve about 100)
With the L/D max point being tangent to a line from the point of origin. (about 140)
Principles of Propulsion
The principles of propulsion are about the same when talking about them in the last chapter.
Newtons 2nd law F=ma
Newtons 3rd law action reaction
Principles of Propulsion
Propeller aircraft process large quantities of air with only a small acceleration of the air when compared to turbojets.
This makes them more efficient than turbojets.
Power Available
There are 4 types of horsepower:
Now they use a dynamometer or dyno.
Power Available
More BHP is required than THP by the plane at any speed because of the loss in efficiency by the prop.
Note on the curve at max speed, where the top of the curves meet at about 165 kts, if you divide 220 by 250 you get a prop efficiency of 88%.
In order to get prop efficiency, use the following equation:
Power Available
Some engines have reduction gearing to slow the prop relative to the engine
There is a resultant loss resulting in shaft horsepower.
Cessna 175 is geared
Power Available
It is less than SHP because the prop is not 100% efficient.
There is a difference between thrust and thrust horsepower
You must use a formula to convert thrust horsepower to thrust.
The formula for doing this is:
Power Available
Converted into thrust horsepower units of course.
Types of Props
Power Available vs Velocity
Brake horsepower and shaft horsepower do not vary greatly with changes in velocity for normal installations.
Some plane manufactures us the extra velocity to ram charge the intake and thus make a poor mans turbo.
Power Available vs Velocity
Thrust horsepower does vary with velocity.
This is because prop efficiency varies with velocity.
Variations with Power and Altitude
3 types of powerplants must be considered:
As a rule, as altitude is increased the temp drop is not enough to offset the loss in density and power is decreased.
A corresponding fuel flow reduction is experienced as well.
Variations with Power and Altitude
These engines are sometimes called altitude engines or critical altitude engines.
The brake specific fuel consumption is the fuel flow related to the brake horsepower of the engine.
It is generally lowest in the 40 to 60% power range and can be found by using the equation:
Variations with Power and Altitude
These engines loose power as they go up in altitude because of the less dense air.
A decrease in horsepower of 50% or more may be possible at altitudes of 18 to 19,000 feet.
Straight and Level
For straight and level, max velocity will occur at the intersection of the full power-available curve and the power required curve
Climb Performance
The different climb vectors all still apply as previously covered in jet performance
Climb Performance
Vx or max climb angle is achieved when excess thrust is at a max.
In order to pin down an airspeed, one must calculate the sine of the corresponding climb angle then plot it against the velocity.
Dole points out that the example shows max climb at stall for the prop whereas the jet is at L/Dmax
Climb Performance
Vy or max rate of climb occurs at the velocity where max excess power occurs.
In other words the greatest difference between horsepower available and horsepower required.
Endurance
Remember to obtain max endurance the min fuel flow is required to stay airborne the max amount of time.
Minimum power required should be the point of minimum fuel flow, this is not L/Dmax but at the point where ________ is at a max.
Specific Range
Remember to obtain max distance, the specific range must be at a max the equation is:
The tangent line drawn to the curve should indicate the max specific range velocity.
For a prop aircraft this is L/Dmax
2 things occur at L/Dmax for a prop plane:
Wind
Wind effects specific range the same way as discussed earlier in the jet performance chapter.
Headwind decreases it
Tailwind increases it
Total Range
Total range is the same as for the Jet performance
Find the average specific range and multiply it by the fuel burned.
pg94 Dole