## POWER CURVES

This post is the basement for explaining the climb, cruise and descend performance of and aircraft. Part of the Private pilot (PPL) and Air Transport Pilot (ATPL) performance course.

### What is the power?

The definition of Power (P) is the work per time unit (P=W/t). Let´s change this formula in a more useful way for us.  As work is Force multiplied by distance ( W=F x d) , power is de force multiplied for distance divided by time (P=F*d/t).

Speed(v) is distance (d) divided by time (t) ( v= d/t). So we can say that the power is the force multiplied by speed (P =F x v).

Although we know there are many forces actuating in a plane (explained in the post: aircraft take off forces). we are going to focus in Drag and Thrust forces.

• Thrust (T): force generated by the power plant, which decreases slightly with speed due to slippage of the propeller. • Total Drag (D): In the principles of flight subject posts it is explained with more detail. The total drag is the result to sum two different kinds of drags, called parasite and induced drag. The speed where the parasite and the induced drag are equal is called the minimum drag speed. So far we know that the Power is a Force multiplied by a Speed (P=FxTAS).

If the force is thrust, we call it, available power ( Pa=TxTAS), and if the force is the Drag, we call it, Required Power.

• Available power (Pa): Is the power of the engine. It is written in the manufacturer specifications of the engine. P=T*TAS.
• Power required (Pr): It is the power required to win the drag in a specific speed. P=D*TAS.

# ### INTERESTING SPEEDS: 1.-Stall Speed (Vs). It is where the Power required and the power available are equal.

2.-Minimum power required speed. It is where the difference between power available and required is maximum.

3.-Maximum level flight speed. It is the maximum speed that an aircraft can reach in a flight level.

### FACTORS THAT AFFECTS THE POWER CURVES :

Weight: if the weight increases

• Pa remains the same ( for example our car has the same power without people inside or full of people).
• Pr increases because we need more power to move the aircraft ( Drag increases). Density Altitude : ( check Density altitude definition)  If DA increases .

• Pa decreases, because the density decreases so the behaviour of the engine is worse.
• Pr Increases, because the True air speed increases so the drag increases. ( you need much more power to move the aircraft) Configuration : Flaps and landing gear.

• Pa : Reamaind unchanged ( A can has the same power with the door open and close)
• Pr: As drag increases, the required power increases. Wind : It doesn´t have any effect neither the Pa nor Pr

• #### Matt Pickett | Oct 3,2020 Reply

Overall I think good, except check your force (or thrust) vs. speed diagram – at low speed, thrust is high; reference, “Aerodynamics for Naval Aviators”. Also, in the video, Gene Benson has made the same mistake by plotting low thrust at low airspeed.

Also, what is the reference for the black & white diagrams please?

Thanks

• #### David Mohammed | Jul 11,2021 Reply

How to calculate the required engine power in Megawatts at a given cruise speed and atmospheric condition.
Number of engines:2
Wing surface: 88.3m
Diameter of engine inlet: 1.1180m
Oswald efficiency: 0.67
Span: 23.7m
Mass: 30000kg
(ISA) Air density at cruise altitude:0.50 kg/m3
Cruise speed: 450kts
Zero-lift drag coefficient: 0.015
For the International Standard Atmosphere (ISA) please use:
Gravity acceleration: 9.80665m/s2
Gas constant for air: 287.00J/kgK
Sea-level pressure: 101325Pa
Sea-level temperature: 15C
Sea-level density: 1.225kg/m3

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