What Happens to The Potential Energy of a Descending Airplane?

A commercial airplane raised to a cruising altitude of, say, 35000 feet, has accumulated a lot of potential energy.

Where does it go when the airplane descends? It can’t all be converted to kinetic energy, since an airplane’s landing speed is less than it’s cruising speed.

Air friction.

When descending the pilot will reduce the throttle, and depending on the airplane and the speed of the descent may extend air brakes to slow the plane down. Extending the landing gear and flaps will also increase the drag. The potential energy is turned into kinetic energy in the descent, but the increase in drag and decrease in throttle means the airplane actually slows down before landing.

that bounce at the end and the loud hot brakes is the last of it.

Some of it gets converted back into jet fuel?

The answer to where does the energy go is almost always the same… heat. Air friction is heat, brakes work by converting kinetic energy into heat, etc. When something loses energy, there is almost always something else getting hotter.

Altitude is stored energy. At 36,000 feet a 747 will glide about 100 miles without engine power.

Think of it this way. The airplane requires fuel to maintain cruising speed. When descending it requires less fuel to maintain that speed. If descending while maintaining speed requires a negative amount of fuel you’ll need to increase air resistance, or you’ll get more kinetic energy.

Answered in one. The plane is pretty slippery, so it can’t descend at a very steep angle without picking up a lot of speed. If you’re on a commercial flight, about 20 minutes before landing you’ll hear the pilot dial back the thrust from the engines. If he maintained level flight, aero drag would result in a gradual reduction of speed. But he chooses a shallow descent, using potential energy to compensate for aerodynamic drag and maintain speed (or at least achieve a more gradual reduction in speed than he would achieve in level flight). If he chooses too steep a descent angle, it’s analogous to driving your car down a steeper hill: the plane will start to accelerate because gravitational potential energy is being converted to kinetic energy faster than aero drag can piss it away.

If you want to descent at a steep angle without building up excessive speed you have to increase aerodynamic drag so that for a given speed, you’re pissing away energy very rapidly. At high speeds, spoilers reduce lift from the wings, allowing the aircraft to fly at a high angle of attack, causing more drag and allowing the aircraft to descend more steeply without picking up speed. At lower speeds, flaps and landing gear may be safety deployed to increase drag.

In the end, the disturbed air in the plane’s wake undergoes viscous dissipation, which means that all of that energy ultimate manifests as heat.

This exactly. It’s amazing how many questions can be answered with this rule of thumb.

Additionally, if say there’s an emergency and the pilots need to ditch some of that potential energy and slow the plane down, they can also “crab” the airplane. I am not a pilot so I don’t know exactly how they do it, but I believe they turn the rudder one way then turn the ailerons the other, so one set of controls is trying to turn the plane one way and the other set of controls is trying to turn it the other way. The plane ends up flying kinda diagonal to the way its nose is pointing (hence crabbing, since it moves kinda sideways like a crab) and the aerodynamic inefficiency of flying this way dumps a fair amount of speed fairly quickly.

Pilots also use crabbing to land in heavy crosswinds. They crab the plane to point the nose in the direction the wind is coming from so that the wind is blowing straight across the wings, even though that’s not the direction that the plane is flying towards. Then just as they hit the runway they “de-crab” and point the nose in the direction the plane is going. There are some very scary looking videos of planes doing this on youtube. In this case they aren’t trying to dump energy. They are just trying to point the nose in the direction the wind is coming from, so they don’t force the controls as far to create more drag.

As a slight hijack, the B-52 can actually turn all of its landing gear so that it can land while crabbing and not have to straighten out as it hits the runway. It continues to crab as it goes down the runway.

This page has a lot more details, and explains in detail the difference between a “sideslip” (crabbing for a crosswind landing) and a “forward slip” (a more extreme crabbing to dump speed or to lose altitude quickly without gaining speed):
http://flighttraining.aopa.org/magazine/2009/January/200901_Features_Slip_Solution.html

Ever see, or feel the turbulence of a passing plane, or truck? Some if the kinetic energy of the vehicle gets transferred to the air.

Crabbing is turning into the wind so that you “kill” your drift - if you try to point your nose without accounting for the wind from the side you will start drifting as the wind pushes you. Now, you do point into the direction the wind is coming from, but not all the way to directly where the wind is coming from or even where the relative wind is coming from (as you go faster the wind vector starts moving toward the front of the plane), but it depends on the aircraft weight. It can be done with flying a different heading or using rudders, but the wings should remain level.

Side slip is the other thing you alluded to; putting your wing into the wind and your opposite rudder (wind down, top rudder was what the Navy taught me), to enable you to still maintain your flight path, while not getting pushed by the wind, and, since you are flying inefficiently, you are increasing drag/lift, causing you to descend at a greater rate if you maintain power settings.

Yeah, some of those youTube vids of folks pointing 15 degrees from centerline, then turning at the last minute are cool. I’ve done it quite a few times, and had new crewmembers frightened, as we would be pointed at off the runway when starting our landing flare.

“Man, that runway was short!”
“Yeah, but it sure is wide”

Badass!

Yep, that’s pretty much it. You can turn an airplane using only rudder - the wings won’t dip much but the direction you’re pointed turns. People in the plane will feel a pull to the outside of a turn like you’re turning in a car on a flat surface. You can also turn with just the ailerons, tipping the wings. You won’t turn as quickly as when you use that along with rudder, and passengers will feel like they’re sliding down sideways into the turn. It’s like being on a banked corner but not having enough speed for that bank. A proper airplane turn is using rudder and ailerons together so that the passengers aren’t pulled either left or right.

So if you cross them in different directions, you’ll go straight, but one wing will be dipped down, and your nose won’t be pointed straight into the airstream. Like you said, this is pretty inefficient and lets you lose a lot of altitude without picking up speed.

When I learned to fly small planes 35 years ago, we learned you crab in a crosswind landing so the plane’s body is aligned with the runway, that way your wheels are pointed the direction they have to be rolling when they hit (and don’t skid sideways). As you approach the runway, you kick enough rudder to align the plane with the runway, but then you’d be moving partially sideways because of the crosswind. So you use opposite aileron to drop the upwind wing, and therefore you fly straight down the runway, but with one wing dipped down. That’s how you’re supposed to land, one side wheel hits first.

Those scary YouTube’s you’ve seen are something different. I have a buddy who’s a commercial pilot, and he tells me that they don’t crab on a crosswind approach, they keep the wings level, and it looks like it’s crabbing to an observer on the ground, but the plane is flying straight into the wind with wings level. They may kick rudder right at the end to begin to align the fuselage, but they’re willing to contact the ground while not pointed right down the runway. He tells me the landing gear can take it, and you don’t have the problem of having one wingtip close to the ground on contact.

Actually, yes, sort of. As mentioned above, the pilot backs off on throttle, so less fuel is consumed.

During normal straight flight, the fuel consumed is equal to the energy lost to air friction. While a jet is pretty slippery, drag is a function of speed squared, so a lot of energy has to be injected to overcome the loss. During descent, you need less fuel because you’re converting potential energy (altitude) into kinetic (forward motion).

But of course, it all ends up as air friction. Still, you land with less fuel consumed during descent, thanks to that potential energy you pumped into the jet during ascent.

I’ll never forget a night landing in a blizzard as a passenger in a turboprop back in the early 70’s, and looking out my window and seeing the runway zooming directly at me at what seemed like a 45 degree angle to the fuselage! (Of course I know it was less, but that’s how it looked.) Right down to the ground, jerking straight at the last minute for a bumpy but safe landing, much to everyone’s relief. For the pilot, probably a non-event, but I’ve flown hundreds of times and that was the most memorable landing. IIRC, the pilot got a round of applause from the passengers.

I think this is the answer. Moving airplane gets converted to moving air. Same with a parachutist. I doubt if there’s much heat conversion.

What do you think “heat” is? It’s just particles moving. Move the particles faster, and you get more heat.