Skydiving physics

[fonz 0]

As a former physics student, I've been thinking lately about the physics that lie behind our beautiful sport.

Is there by any chance a mathematician here who is adept at solving non-linear second-order differential equations?

Further, I've been philosophising about whether or not you should theoretically be able to fly upside down under canopy. And here I mean sustained inverted flight, not performing rolls and loops. Personally, I think that the canopy itself, being a wing, should be able to do this, but since the lines are not rigid, could one prevent falling into the canopy provided that you have enough airspeed?

And five hundred entirely naked women dropped out of the sky on parachutes.
-- The Hitchhiker's Guide to the Galaxy

[piisfish 135]

There's a couple of pics of CReW formations with a canopy flying inverted and 1-2 canopies flying a stack. I don't know the name of that formation/figure... but the canopy flies.

If it comes to solo inverted flights with rigid lines (if that was possible), to keep the balance would be quite challenging

scissors beat paper, paper beat rock, rock beat wingsuit - KarlM

[fonz 0]

So apparently it is possible. But then I wonder how you would prevent falling into your canopy. Would it just be airspeed, or is there more to it?

And five hundred entirely naked women dropped out of the sky on parachutes.
-- The Hitchhiker's Guide to the Galaxy

[kallend 1,623]

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As a former physics student, I've been thinking lately about the physics that lie behind our beautiful sport.

Is there by any chance a mathematician here who is adept at solving non-linear second-order differential equations?

Further, I've been philosophising about whether or not you should theoretically be able to fly upside down under canopy. And here I mean sustained inverted flight, not performing rolls and loops. Personally, I think that the canopy itself, being a wing, should be able to do this, but since the lines are not rigid, could one prevent falling into the canopy provided that you have enough airspeed?

Current canopies could not achieve sustained inverted flight (even if you solved the line rigidity problem) because

(1) the intakes are in the wrong place. The intake has to be located such that the stagnation point of the airflow is over the opening.

(2) with the CG way above the lifting surface, it would be wildly unstable in both pitch and roll.

(3) the lift force would place the fabric in compression laterally, instead of tension, which would collapse the canopy.

(4) to solve these would require redesign to the extent that the resulting device would no longer be recognizable as a canopy.

Which particular non linear 2nd order PDE do you wish to solve?

...

The only sure way to survive a canopy collision is not to have one.

[slotperfect 7]

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There's a couple of pics of CReW formations with a canopy flying inverted and 1-2 canopies flying a stack. I don't know the name of that formation/figure... but the canopy flies.

The two names I have heard used are "pendulum" and "drag plane." The inverted canopy is not completely upside down, however. If you look at the attached pic, you will see that there is a definite angle at which the formation flies. Flown directly at a crowd, like at an airshow, it does in fact look as if the bottom canopy is completely upsaide down.

It is a lot of fun being on the bottom . . . it is NOT fun, however, being the one in the middle having to hold onto my big ass.

Arrive Safely

John

[diablopilot 2]

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As a former physics student, I've been thinking lately about the physics that lie behind our beautiful sport.

Now there is the begining of trouble!

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could one prevent falling into the canopy provided that you have enough airspeed?

No. Not unles the force on the body pulling away from the canopy is greater than the weight of the body, no matter if it's gravity or centrifigal. Otherwise you'll fall towards the canopy, just like a helicopter can't fly inverted.

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You're not as good as you think you are. Seriously.

[quade 3]

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. . . just like a helicopter can't fly inverted.

Uh . . . you mean full scale helicopters. (It's a materials issue.)

Model helicopters can fly inverted as long as the pilot has enough skill as so could a full scale helicopter if it was designed to do so by beefing up the rotors and all the other gak associated.

http://www.scienceweb.org/movies/bluethunder.html

quade -
The World's Most Boring Skydiver

[diablopilot 2]

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so could a full scale helicopter if it was designed to do so by beefing up the rotors and all the other gak associated.

You'd end up with something that was probably too heavy to get off the ground....it's not just a matter of scaling a model. You'd need to make longer and longer rotors to create more lift to get the beast in the air and eventualy your blades would be so long the tips would be supersonic even at low RPMS. That would kill the lift right there......

The Lynx (British built) is capable of some pretty radical manuvers including a barrell roll......

The point being sustained inverted flight with a modern parachute is not possible. I have done a barrell roll and it's probably as close as you'll get. BTW getting slack line is not for the faint of heart.

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You're not as good as you think you are. Seriously.

[quade 3]

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You'd end up with something that was probably too heavy to get off the ground....

Which is essentially what I meant by "materials issue" and not just of the rotors but all the, as I said, associated gak (which is a technical term meaning junk). You'd need -stronger- materials so that you could keep essentially the same weight. Rotor length isn't an issue and neither is horsepower. The issue is cost and there is NO market for aerobatic helicopters (although I should show you a video tape I shot of one in 1988 doing some pretty nifty aerobatics).

Getting back to sustained inverted canopy flight . . . simply not possible . . . at all.

quade -
The World's Most Boring Skydiver

[kallend 1,623]

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As a former physics student, I've been thinking lately about the physics that lie behind our beautiful sport.

Now there is the begining of trouble!

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could one prevent falling into the canopy provided that you have enough airspeed?

No. Not unles the force on the body pulling away from the canopy is greater than the weight of the body, no matter if it's gravity or centrifigal. Otherwise you'll fall towards the canopy, just like a helicopter can't fly inverted.

I have a helicopter that flies inverted just fine. It's radio controlled.

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The only sure way to survive a canopy collision is not to have one.

[diablopilot 2]

Sometimes you might be just a little TOO literal.


We weren't playing with toys today....

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You're not as good as you think you are. Seriously.

[fonz 0]

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(1) the intakes are in the wrong place. The intake has to be located such that the stagnation point of the airflow is over the opening.

Good point you raised here. In fact, I hadn't even considered that. This is what makes a canopy different from an airplane wing: it has openings in order to inflate, that's where it gets its rigidity from in the first place.

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(2) with the CG way above the lifting surface, it would be wildly unstable in both pitch and roll.

Indeed. That's why airplanes with wings at the bottom (or below) of the fuselage are very rare. They're just hell to fly.

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(3) the lift force would place the fabric in compression laterally, instead of tension, which would collapse the canopy.

Elaborate.

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(4) to solve these would require redesign to the extent that the resulting device would no longer be recognizable as a canopy.

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Which particular non linear 2nd order PDE do you wish to solve?

Consider this:

m * dv/dt = (c * A * ( rho0 + drho * x ) / 2 ) * v^2 - m * g

Here m, c, A, rho0, drho and g are constant, so it comes down to

dv/dt = alpha * v^2 + beta * x * v^2 + gamma with alpha, beta and gamma constants.

Obviously, v = dx/dt and we need both x(t) and v(t).

This is the physical description, to a mathematician it might look more familiar if we take
x(t) -> f(x)
v(t) -> f'(x)
so we get
df''/dx = alpha * (f')^2 + beta * f * (f')^2 + gamma
and need f(x) and f'(x).

To me, it's the dependence on x that makes it such a bitch. But taking the air density constant during an entire skydive is something you simply don't get away with.

The first one to solve this sucker gets a case of beer and gets credited on the site I'm building about skydiving physics

And five hundred entirely naked women dropped out of the sky on parachutes.
-- The Hitchhiker's Guide to the Galaxy

[falxori 0]

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m * dv/dt = (c * A * ( rho0 + drho * x ) / 2 ) * v^2 - m * g

ok, thats where i refuse to follow this thread any more !

"Carpe diem, quam minimum credula postero."

[kallend 1,623]

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(1) the intakes are in the wrong place. The intake has to be located such that the stagnation point of the airflow is over the opening.

Good point you raised here. In fact, I hadn't even considered that. This is what makes a canopy different from an airplane wing: it has openings in order to inflate, that's where it gets its rigidity from in the first place.

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(2) with the CG way above the lifting surface, it would be wildly unstable in both pitch and roll.

Indeed. That's why airplanes with wings at the bottom (or below) of the fuselage are very rare. They're just hell to fly.

No, they aren't, but they almost always have significant dihedral for roll stability, which an inverted canopy would not have. They also have a tail for pitch stability, which an inverted canopy would not.

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(3) the lift force would place the fabric in compression laterally, instead of tension, which would collapse the canopy.

Elaborate.

You are the (ex) physics student - draw the vector diagram and resolve the forces horizontally.

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(4) to solve these would require redesign to the extent that the resulting device would no longer be recognizable as a canopy.

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Which particular non linear 2nd order PDE do you wish to solve?

Consider this:

m * dv/dt = (c * A * ( rho0 + drho * x ) / 2 ) * v^2 - m * g

Here m, c, A



The first one to solve this sucker gets a case of beer and gets credited on the site I'm building about skydiving physics

Please send it to me, then, since I already did it in two dimensions, not just one, and posted the results.

Take a look at www.iit.edu/~kallend/skydive

PS ever hear of Messrs Runge and Kutta?

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The only sure way to survive a canopy collision is not to have one.

[EBSB52 0]

"You are the (ex) physics student"



Watch out, nerd fight! JK, I majored in Justice because I'm a math idiot!!!

[speedy 0]

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Consider this:

m * dv/dt = (c * A * ( rho0 + drho * x ) / 2 ) * v^2 - m * g

I find it utterly amazing that anyone would even want to consider the above

Dave

Fallschirmsport Marl

[nicknitro71 0]

x = (1/distance* beta) - (alpha/beta) - (gamma/beta * 1/V^2)

Am I even close?

Memento Audere Semper

903

[billvon 2,400]

>That's why airplanes with wings at the bottom (or below) of the fuselage
>are very rare. They're just hell to fly.

?? Most aircraft are low-wing. Go to any large airport to verify.

[dorbie 0]

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Indeed. That's why airplanes with wings at the bottom (or below) of the fuselage are very rare. They're just hell to fly.

No they're not, most tend to have a dihedral wing configuration that helps their roll stability.

[pilotdave 0]

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Indeed. That's why airplanes with wings at the bottom (or below) of the fuselage are very rare. They're just hell to fly.

No they're not, most tend to have a dihedral wing configuration that helps their roll stability.

In fact, high wings and swept wings produce effective dihedral. Too much of that effect leads to "dutch roll," kind of swaying in roll and yaw...very uncomfortable for passengers. Thats why high swept wing aircraft need anhedral.

Almost every modern business jet has the fuselage sitting on top of the wing, so the spar doesn't have to pass through the fuselage. Then they just put a fairing over the wing-fuselage joint. They seem to fly alright.
Dave

[dorbie 0]

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Indeed. That's why airplanes with wings at the bottom (or below) of the fuselage are very rare. They're just hell to fly.

No they're not, most tend to have a dihedral wing configuration that helps their roll stability.

In fact, high wings and swept wings produce effective dihedral. Too much of that effect leads to "dutch roll," kind of swaying in roll and yaw...very uncomfortable for passengers. Thats why high swept wing aircraft need anhedral.

Almost every modern business jet has the fuselage sitting on top of the wing, so the spar doesn't have to pass through the fuselage. Then they just put a fairing over the wing-fuselage joint. They seem to fly alright.
Dave

I hoped I made it clear from the quote that my comment referred to low wing designs mentioned in that quote.

[pilotdave 0]

Uh huh. I was just adding to it.... that high wings can cause stability problems of their own.

Dave

[fonz 0]

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?? Most aircraft are low-wing..

No offense, but I've seen, ridden, jumped or in some cases even flown the following aircraft:

Cessna 208 Caravan
Cessna 206
Cessna 182
Twin Otter
Skyvan
Turbo Let
Dornier
ASK 21 (a sailplane)
Boeing 767

Of these (and others I failed to mention), only the latter has low wings unless I accidentally stepped through a rift in the universe so that I now find myself in a parallel space-time continuum where the definitions of high/low and top/bottom differ from where I came from

And five hundred entirely naked women dropped out of the sky on parachutes.
-- The Hitchhiker's Guide to the Galaxy

[kallend 1,623]

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?? Most aircraft are low-wing..

No offense, but I've seen, ridden, jumped or in some cases even flown the following aircraft:

Cessna 208 Caravan
Cessna 206
Cessna 182
Twin Otter
Skyvan
Turbo Let
Dornier
ASK 21 (a sailplane)
Boeing 767

Of these (and others I failed to mention), only the latter has low wings unless I accidentally stepped through a rift in the universe so that I now find myself in a parallel space-time continuum where the definitions of high/low and top/bottom differ from where I came from

Here is a more representative set of airplanes produced in large numbers. Most of the airliners and fighters are low wing, but 36,000 Cessna 172s can't be ignored. Then there are many other Cessna high wing aircraft too. 6000 Sopwith Camels!


Civil airliners

Douglas DC-3:1935 to 1945, 13,400, including about 2500 built in the Soviet Union.
Boeing 737: over 5000 built from 1967, still in production.
Airbus A320 family: almost 3000 built from 1988, still in production.
Douglas DC-9: over 2400 of the DC-9/MD-80/MD-90 and Boeing 717 family of aircraft made from 1965 to date. Still in production.
Fokker Friendship, 786 Friendships were delivered between 1958 and the mid 1980s, making it the most successful Western turboprop airliner to date, evolved into the Fokker 50 and Fokker 60 airliners with more efficient engines but a lower production run.
Boeing 747:over 1000 built by 1990s from its start in the 60s. Still in production.

General aviation

Cessna 172: 39,600 manufactured between 1955 and 2002, still in production.
Piper Cherokee: first manufactured in 1960, still in production
De Havilland Tiger Moth: 1931 to 1957, 8492.
Antonov An-2: widespread and long used light transport biplane, 1949 to 1996, about 20,000+
Fighters

Propeller driven fighters
Messerschmitt Bf 109: 1937 to 1945, 35,000.
Supermarine Spitfire: 1938 to 1947, 20,351 plus 2408 of the navalised Seafire.
Focke-Wulf Fw 190: 1940 to 1945, 20,051.
Republic P-47 Thunderbolt: 1941 to 1945, 15,660.
North American P-51 Mustang: 1940 to 1945, 15,675.
Hawker Hurricane: 1937 to 1944, 14,449.
Curtiss P-40: 1938 to 1944, 13,378.
Vought F4U Corsair, 1942 to 1953, 12,571.
Sopwith Camel: 1916 to 1918, 6000.
Polikarpov I-16 Rata: 1933 to 1940, 8644.

Jet fighters
F-16: about 2,900 still in production. In service with many countries.
F/A-18 Hornet: Widespread modern jet fighter
Hawker Siddeley Harrier: versatile VTOL jet plane with both ground and attack and fighter variants.
F-4 Phantom widely used multirole aircraft: 1962 to 1979, 5,000+.
MiG-15: simple and widespread early jet fighter: 1948 to ?,
MiG-21: the most numerous and widely used jet fighter in the world: 1958 to ?, about 10,000+

Close support/ground attack aircraft

Junkers Ju 87 Stuka: successful WW2 dive bomber.
Ilyushin Il-2 Shturmovik: successful ground-attack plane, 1940 to 1944, 36,163
Hawker Typhoon: fighter plane, known for its anti-tank usage
A-10 Thunderbolt II: highly successful ground-attack airplane.

Bombers

Consolidated B-24 Liberator: 18,482
Boeing B-17 Flying Fortress : 12,726.
Boeing B-52 Stratofortress, 50 years in service, may end up being 100 years.
Vickers Wellington: 1937 to 1945, 11,461.
Avro Lancaster: 1941 to 1945, 7377. Design evolved into the Lincoln bomber and the long-serving Shackleton maritime patrol aircraft.
De Havilland Mosquito: multirole fast bomber / fighter, 1940 to 1950, 7781.
Junkers Ju 88: multirole bomber / fighter
English Electric Canberra: An early twin-jet bomber, with variants still in active service for reconnaissance purposes. Sold by the UK to USAF as the B-57.
Ilyushin Il-28: simple and widespread early jet bomber

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The only sure way to survive a canopy collision is not to have one.

[pilotdave 0]

High wings are less common in general. They have certain disadvantages over low wings. But they have some advantages too... You'll see a lot more high winged bush planes or anything designed to land on rough strips, like a twin otter (or single otter or beaver or porter, etc...).

There are some high winged large aircraft...but mostly military aircraft. There's a structural disadvantage... there's no easy place to mount the main landing gear on a high wing, so they tend to end up heavier. But lifting the engines up is better for taking off from rough strips to keep debris out of the engines or props. Also lifting the engines up higher loows for kneeling landing gear, like the C-5 or An-124 have.

In small planes, they're a lot more common, but still less common than low wings. Cessna has always stuck with em for their singles. They also use wing struts in most of their designs, which saves a bit of weight but adds drag.

The point is that there are a lot of high wing aircraft out there...but the reason is not because low wing aircraft are difficult to control. Most aircraft are in fact designed with low wings.

Dave