# 'Distanceless' force for aircraft seems to break laws of physics

When an jet is flying, its engines produce thrust. I assume that the thrust and fuel consumption is about the same at all aircraft speeds. However, when the airplane is going faster, it produces more power, because $$W=fd$$, and more distance is covered in one second. Theoretically, the velocity, and therefore the power, could increase indefinitely. The airplane's force seems to be a 'distanceless' force, while a car has to reference the ground. The car has to increase its power input by a factor of 2 to sustain twice as great a speed, assuming constant air resistance.

This appears to break the first law of thermodynamics, because it seems that you are getting more work done with a constant fuel input. Is there a mechanism by which more power is needed for the airplane at higher speeds, making it fit with the law, or is my reasoning wrong? Sorry if this sounds confusing. Thank you!

• Planes fly with respect to the air they are in. And air moves more easily of it's own accord than the ground (unless you are on a treadmill) so it may be difficult for you to grasp distance in that scenario. In which case, just take a a time derivative of work to get power which converts distance turns into a velocity. Alternatively, you can you can just think of the case where the plane is flying in static air (no wind) and consider all relative motion between aircraft and wind as being due to the motion of the aircraft flying through the air. Aug 8, 2022 at 15:40
• Velocity can not increase indefinitely, speed of light will stop any airplanes from going faster eventually, even if we assume infinite fuel and no friction. Furthermore jet engines work like rocket engines, so they don't need a surrounding medium to move. Aug 8, 2022 at 15:47

The constant power of a jet engine is only approximate, and only valid over a certain range of speeds. Really it speaks to the fact that the jet is fairly inefficient at slow speeds.

When stopped or slow, the engine is throwing a huge amount of heated gas rearward. Most of the chemical energy of the fuel is going into the KE of the exhaust. Only a small amount is going into accelerating the airframe.

As the craft gains speed, the power developed by the engine stays approximately the same, but (in the ground frame), more of the power goes into the airframe and less goes into the energy of the exhaust.

Nope. Here's what you are missing.

A plane's engines develop thrust (a force) by imparting a momentum change to the air flowing through them. That thrust propels the plane against the friction force generated by the air flowing past it.

That friction force depends on the square of the plane's speed through the air, so doubling the speed increases the friction force by a factor of four. And the associated math dictates that the horsepower required to propel the plane depends on the cube of the speed, so if we want to double the plane's speed we need 8 times the horsepower.

Since horsepower is determined by the flow rate of fuel being burned in the engine, doubling the speed of the plane requires the engine to burn 8 times as much fuel per hour.

• Thank you! I assume you mean that power is cubed because of the increased air resistance, and also the increased distance. But planes or rockets seem to produce the same force independent of the speed, therefore only requiring 4x the power. I wonder if the added power of having to accelerate the fuel provides the other 2x? Aug 8, 2022 at 17:24
• Nope. Remember that power = (effort variable) * (flow variable); here we have thrust as the effort and feet per second as the flow which furnishes three powers of velocity in the expression for power. For more info see the aviation stack exchange. Aug 8, 2022 at 17:42