How can speed and power be made independent in an airplane?

Question

I heard a piece of information many years ago, and the more I think about it, the less it makes sense. It was like:

When airplanes what to raise altitude, they do not increase speed, but they increase power. It is like when going up a hill, you do not walk faster, you just push harder.

Now, I understand the statement at an intuitive level. I understand what it means for me to go up a hill, because I know what I feel.

But things are quite different with motorized vehicle in general, and maybe with airplanes in special.

My understanding is that the following equation is (relatively) true (at least as a principle):

power = rpm * torque

and my understanding is that

speed = rpm * coef

so in the end

power = f(speed)

or

speed = f^-1(power)

where f is mostly (?!) multiplicative, or at least linear(-ish).

Now, how can be power increased, without increasing speed?

This statement comes to confirm that I miss some information, since the general knowledge defies my formulas :)

There are two parameters that an A/T can maintain, or try to attain: speed and thrust. (I understand that thrust is power).

The only way I can explain it is like this (and I need some confirmation):

The (pilot) "asks" to increase the rpm (as a base parameter, speed and power being derived parameters). In vacuum, all the energy is used or increase RPM, so power and speed remain proportional. But in the real world, and especially during flight, a lot of the energy is used or lost in many places. So speed and power no longer remain proportional, the difference being lost (e,g, to friction).

Additionally, please provide a better explanation of what I just wrote. I am really interested to understand the basics of this topic.

Basic formulas are OK. (Complicated) Integrals and derivatives should be avoided please :)

Notes:

I am not (by far) a mechanical engineer whatsoever. As a hobby, I practice "mental" mechanical engineering - trying to understand how some things can be designed; or trying to understand how some things are implemented. My background is more related to electric / electronics, software, management.
In the example with a man climbing a hill, my explanation makes some sense (to me): I prepare to increase the speed by using more power, then I make a short break to rest the leg, and to move to the other leg, and then again use higher power and so on. It is mostly like a human-implemented PWM. This is how the speed can remain constant, while the power increases. But how does this work for the engines / airplanes?
I am quite sure that ultimately everything is related to how much fuel is burned in the unit of time. Unless I am wrong.
My knowledge about airplanes and flight are limited at best, even though I understand some principles.

I have in mind 2 examples: 1. a screw being screwed in a properly threaded hole; 2. The car moving on a road: as long as the gears do not change, and wheels do not slip, speed=rpm*coef, where coef depends especially on the gear details and wheel sizes. — virolino, Oct 14 '20 at 12:37
In an aircraft in straight and level, unaccelerated flight, all of the forces of flight are balanced. Changing the pitch of the aircraft without changing any other control will cause a change in speed. Changing the power setting without changing any other control will change the aircraft’s propensity to climb or descend. Functionally, this means that if you increase your power in a plane that is trimmed out for a certain airspeed, the nose will rise and the plane will climb. If you decrease the power, the nose will fall and the plane will descend. In both cases, the airspeed remains constant. — Dean F., Oct 14 '20 at 12:38
@virolino Those examples are different because a screw and a car tire (at least usually) do not slip, meaning any motion of the tire directly translates to a motion of the car. When the tire starts slipping, this is no longer true. In an aircraft, the propeller kind of slips in the air all the time. — Bianfable, Oct 14 '20 at 12:40
@Bianfable: "In an aircraft, the propeller kind of slips in the air all the time." - that is one of the basics, where I have intuition, but not explanation. — virolino, Oct 14 '20 at 12:42
Also, your examples of a screw and a car are a little too simplistic to apply to aerodynamic forces. The propeller of an aircraft has aerodynamic forces acting on it. Several factors will affect it like density altitude for instance. For example, an aircraft on the ground with its brakes on will not increase its speed regardless of power setting or prop rpm. Also, power setting and prop rpm in a plane with adjustable props are linked, but not linearly/directly dependent on each other. — Dean F., Oct 14 '20 at 12:44
@DeanF.: I can understand the car dynamics relatively good (at least at a macro level). Basically, a car has a steering wheel which steers the front wheels to choose direction, and has 2 pedals to decide the RPM, and thus speed. However, the airplane is a totally different monster. I do not understand how everything fits together, and I hoped for a more "basic" explanation. I am not sure how to explain my level of understanding. — virolino, Oct 14 '20 at 12:45
@DeanF.: you are right, a screw is a tad simpler than an airplane, I am aware of that :) But my level of knowledge and understanding is closer to the screw and car, and farther from the plane. — virolino, Oct 14 '20 at 12:47
I just understood the kind of explanation that I need: airplane's speed and power for dummies :D Disclaimer: I am the dummy ;) — virolino, Oct 14 '20 at 12:50
Actually, you are little off on your understanding of cars as well. A car has one peddle to control power. The power tangentially controls the speed. You have to use a sufficiently large amount of power to accelerate. Once you are at your desired speed, you only have to use enough power to counter friction and drag. If I am cruising at highway speeds, friction and drag will eventually slow me down. On the other hand, I have a hill on my route home. To maintain constant speed, I have to increase power when reaching that hill. Just like an airplane. — Dean F., Oct 14 '20 at 12:56
@DeanF.: about the car pedals, you are right, I wrote stupid (even thought I actually have the good understanding). About going uphill -that is where I miss something. I use the same action (push the pedal) to modify either speed or power, right? How are they related? Or independent? (I ignore the trick of using the gear box for easier climb). (I drive a manual gearbox car, so the car does not change any gears for me). — virolino, Oct 14 '20 at 13:06
Airplanes have two controls that control the thrust force of the prop-engine configuration. One controls the power generated by the engine. The other controls the prop angle. Airplane engines are fixed to their props either directly or by a fixed, non-adjustable gear set. The engine’s torque directly counters the air resistance of the spinning prop. The air resistance is determined by the prop angle setting. This, in turn, determines the RPMs of the prop. A combination of angle and rpm determines the amount of thrust force generated. — Dean F., Oct 14 '20 at 13:10
Also, a car’s engine rpm does not directly relate to its wheel’s rpm. There is a relation per gear chosen. Whether automatic or manual, the RPMs will change based on the gear selected. Regardless, the power is determined by the amount of fuel you meter out to the engine using the throttle. The less force that you need, the less fuel you meter. For instance, when traveling away from my house, I have to completely bring my engine to idle in order to go down the same hill without going too much over the speed limit. same with airplanes. And, I drive both automatic and manual transmission cars. — Dean F., Oct 14 '20 at 13:17
I throught (I am not a pilot) that: if a pilot adds power, but keeps the altitude constant, speed must increase; if a pilot adds power, but keeps the speed constant, the plane must rise. — CGCampbell, Oct 14 '20 at 14:35
@CGCampbell - You are entirely right (sort of). In order to keep the altitude constant when adding power, adjustments have to made in other controls to adjust attitude (pitch). If the only adjustment to the aircraft you make is in the throttle setting (power), the airplane will naturally seek a balance in the four fundamental forces of flight, resulting in a climb or descent. Speed will remain constant. — Dean F., Oct 14 '20 at 14:40
@CGCampbell, your intuition is spot on. This really isn't a difficult concept, the OP is way overthinking this... — Michael Hall, Oct 14 '20 at 16:52

score 8 · Answer 1 · answered Oct 14 '20 at 13:48

The problem is your assumption of

speed = rpm * coef

This is only true as long as there is a rigid connection between the RPM and the medium against which the speed is measured.

Let us consider a car for a moment. In a fixed gear, there is a fixed relationship between the engine RPM and the RPM at which the tires rotate. As long as the tires are not skidding, this will directly translate to a motion w.r.t. the road (against which speed is typically measured for a car). This results in the linear equation you show.

This is however not true for an airplane, where the propeller RPM does not directly translate to a speed w.r.t. the air because air is not a solid (otherwise it would be true and you can think of the propeller as a a screw that drives into the solid). Air can flow through the propeller without moving the plane. Consider e.g. a plane that is tied down on the ground and therefore cannot move w.r.t. the ground. You can still start the engine and run the propeller, which creates an airflow behind the propeller, but does not cause any movement. The same could not work with a car, as long as the tires are not allowed to skid.

In flight, the accelerated airflow behind the propeller creates thrust, which is a force that can accelerate the aircraft forwards. The actual motion will also depend on the aerodynamic forces (lift and drag) as well as gravity of course. A higher propeller RPM (at the same blade angle) will give you more thrust, but there is no rigid connection to speed.

score 3 · Answer 2 · answered Oct 14 '20 at 20:37

Now, how can be power increased, without increasing speed?

Think of the airplane for a moment as a black box. It moves through air, creating a drag force. This drag force needs to be overcome by supplying a thrust force which works in opposite direction. Basic physics, equilibrium of forces, no integrals required.

Moving an object against a resistive force needs work $W$ to be done. For our black box aircraft, this work is the drag force $D$ times a distance $s$. Or the thrust force $T$ times $s$, because the forces have the same absolute value. So for unaccelerated, steady, horizontal flight we can calculate the work: $$W = T\cdot s$$ Quick unit check: Drag and thrust are measured in Newton, which is a kilogram times meter per second squared in basic SI units, speed in meters per second and work is either measured in Joule, Watt-seconds or Newton-meters. Check.

Now the black box aircraft climbs. This needs additional work to be done on that aircraft, and if speed does not change, an additional term must be added. The work for lifting the mass $m$ by a height $h$ against Earth's gravitational acceleration $g$ comes on top: $$W = T\cdot s + m\cdot g\cdot h$$ or, expressed in terms of thrust required: $$T = D + m\cdot g\cdot \frac{h}{s} = D + m\cdot g\cdot \frac{v_z}{v}$$

where $v_z$ is vertical speed. Without vertical speed, we get the equilibrium for horizontal flight. Going up requires more thrust (positive $v_z$) and going down requires less (negative $v_z$) than in horizontal flight.

Power $P$ is the derivative of work over time: $$P = D\cdot v + m\cdot g\cdot v_z$$ So the answer is: By varying vertical speed, you vary power while maintaining flight speed.

What that means technically for the propeller: It needs to accelerate the mass flow going through its disk more in order for the airplane to climb or less in order for it to sink. By changing engine torque, the pilot controls by how much that air is accelerated. In a fixed-prop airplane this means that the prop will spin at a different speed (faster for climbing, while flight speed is constant) and for variable-pitch propellers adding torque will increase the prop pitch so it will shovel more air past it per revolution (while keeping prop RPM and flight speed constant).

score 2 · Answer 3 · answered Oct 14 '20 at 13:53

To fully understand the answer you are striving to get, you have to understand the four fundamental forces of flight. These are best explained in the Pilots Handbook of Aeronautical Knowledge. It will explain more about the forces interaction. The ones you are most concerned with are thrust and drag. Thrust is a function of the engine-prop combination, not necessarily power alone.

quiet flyer · Answer 4 · 2020-10-14T15:25:32.893

Start by studying gliders -- note that while they cannot maintain a climb in the absence of updrafts, they can certainly be flown at a wide range of airspeeds, with no influence from a motor at all.

An airplane is nothing more than a glider with power added. Fundamentally, the power setting governs the climb or descent rate for a given airspeed, but doesn't directly govern the airspeed.

Nor does the airspeed directly govern the power output.

In the simple case of a fixed-pitch prop, your suggestion that we can get more rpm and thus more power out of the engine by going faster is correct, but any suggestion that we generally ought to increase speed in order to climb would be incorrect, because it would completely overlook the increased drag that always comes with increased speed.

As for your intuitions based on going up a hill in a car--

Think about what happens when you downshift gears in a car. RPM goes up and the engine can put out more power for a given forward speed. Since the propeller is not rigidly connected to the air, there are two ways we can "downshift" in a propeller-powered airplane.

In an airplane with a simple fixed-pitched prop, simply advancing the throttle will cause the engine to turn faster for a given forward airspeed. The fact that there is some "slipping" between the prop and the airstream is what allows the prop rpm to be increased without increasing the airspeed in this case. And bear in mind that the pilot can always control the airspeed independently of the prop rpm, by pitching the nose up or down, or to put it another way, by adjusting the angle-of-attack of the wing. The airplane may have its own "idea" of what "ought" to happen when the throttle is advanced, but the pilot can always override that inherent tendency and make it do something else. Starting from level flight, if airspeed is held constant and the throttle is advanced, the aircraft must climb.
If the prop blade angle may be mechanically varied, then we also have the option of advancing the throttle and increasing the engine power output without any change in engine rpm or prop rpm.

Let's return to this idea for a moment--

The airplane may have its own "idea" of what "ought" to happen when the throttle is advanced, but the pilot can always override that inherent tendency and make it do something else.

Many people share the impression that if we move the throttle or power lever forward in an airplane, the natural tendency is for the aircraft's speed to increase. Even if we understand that the prop rpm is not rigidly coupled to the airspeed, we still might think that there is some tendency in this direction, based on our experience in driving a car up a hill, etc. In reality, the stability dynamics in an airplane are completely different from the dynamics of driving a car. In many aircraft, advancing the throttle or power lever tends to cause the nose to pitch up so much that the airspeed actually decreases, if we don't do something with the control stick or control yoke to counteract this. In other aircraft, advancing the throttle or power lever does tend to cause the airspeed to increase, if we don't do something with the control stick or control yoke to counteract this. In all cases the pilot is free to override these tendencies and make the aircraft fly at the most desirable airspeed for the climb. The airspeed he or she selects will vary depending on whether he or she wants to climb as steeply as possible or as quickly as possible, and the choice of airspeed will be accomplished by manipulating the elevators via the control stick or control yoke, not by adjusting the throttle or power lever.

Also, you said--

I am quite sure that ultimately everything is related to how much fuel is burned in the unit of time. Unless I am wrong.

It all depends on what parameters we constrain to be constant. It is certainly possible to burn more fuel per unit time flying horizontally than climbing. But if we constrain the wing's angle-of-attack to be constant -- which for shallow to to moderate climb angles, is essentially the same thing as constraining the airspeed to be constant -- then the climb rate will end up being related to the fuel burn per unit time.

In these kinds of discussions, a key issue is what parameters are being held constant and what parameters are allowed to vary. For example, if the pilot is holding the airspeed constant while varying the power setting, the results will be different than if the pilot is holding the pitch attitude constant while varying the power setting, but in neither case will the aircraft's natural pitch stability dynamics come into the picture. If the pilot is varying the power setting while keeping his hands off the control yoke and making no changes to the elevator trim, then it's a different story, but likely not the one you are asking about.

score 2 · Answer 5 · answered Oct 14 '20 at 14:59

Regarding the question about raising altitude and increasing power, airplanes are no different from cars or people: To transfer from level movement to one that has a vertical component, you are going to need more power to maintain the same speed.

The need to increase power in all of the aforementioned cases comes from increasing the potential energy as we (with or without a vehicle) are gaining altitude. We are ascending in earths gravitational field, and to do this, we must do work. This work comes on top of the work we are doing to maintain speed.

There is no running away from gravity, so if we want to ascend, and do not increase the amount of work (power), there will be less work available for going forward, so we will slow down, and depending on climb gradient, come to a stop.

In the case of an airplane, slowing down will become problematic as staying in the air is dependent on speed. At some point the forward speed will not be sufficient for the wings to create lift, and the aircraft will stall and begin to fall from the sky.

Friction, air resistance (or drag), slipping of the tyres or propeller are basically a separate phenomena from the need to increase power to ascend.

score 0 · Answer 6 · answered Oct 14 '20 at 14:22

In level flight if you increase power, speed will indeed rise.

If you are talking about rising the RPM with a constant speed propeller, the speed will only slightly change (because the engine may produce a different power output at a different RPM).

Changing RPM in a constant speed propeller does not produce great changes of power. It's just like selecting a different gear in a manual transmission withouth changing the accelerator value. Changing Manifold Pressure (the throttle lever) will.

How can speed and power be made independent in an airplane?

6 Answers6