Skydiving Modelling

[Unparagoned 0]

Hi, I've finished my second year of my Mathematical Physics Degree and I'm thinking about a project to do over the summer. I was thinking about trying to do a very basic model of when someone is tracking. I've seen here some people say that in the atmonauti angle you can track further than in a flat track, and others say the opposite. Even then if one side is right, which angle to the horizontal do you want to track at, 1, 5, 15 degrees? The steeper the angle you get more drive and travel faster but you reduced lift and vice versa. Also the faster you go the more drag you get, etc. I doubt it is possible to do this analytically so I would be solving it using c++. On the physics side I plan on simply using newtonian physics to calculate lift and drive, and use some drag formulas for the drag for the relative wind direction...
I've only briefly gone through the idea and it may change dramatically. I doubt I will be able to get data that is useful quantitatively but you should be able to get some qualitative information which could be useful. e.g. 7 degree to the horizontal is the idea track position(assuming you are a solid rectangular sheet :P) Even if it doesn't give any useful results it will be a nice exercise for me.

Has anyone done anything like this before? Are there any useful libraries dealing with fluid flow that could make it much easier to do? What do you guys think overall, is it a waste of time, should I do it on something else?

[mr2mk1g 10]

How about using a number of rectangular blocks in a wind tunnel/computer model?

Use one large block for the body and 4 smaller blocks representing the legs.

Simply model the lift/drag etc of the blocks arranged in an almost straight line (as in during a conventional track) then model the lift/drag etc of the blocks arranged in an atmonauti position.

Because they're blocks you still produce figures you can work with (I presume) but you're also producing results which should broadly mirror those which you might expect in real flight.

Then repeat at different angles etc and find the best for each. A comparison of the results of the best position obtained from each should show which is "better" - atmonauti or tracking.

[BIGUN 1,424]

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I've finished my second year of my Mathematical Physics Degree and I'm thinking about a project to do over the summer.

First mistake... you spend too much time in the house. Go outside and play.

PM Dr. Kallend, Winsor or BillVon with a hyperlink to this thread so they can all take a peek at it. I'm sure out of all of them, you're bound to get some guidance.

Nobody has time to listen; because they're desperately chasing the need of being heard.

[LearningTOfly 0]

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I've finished my second year of my Mathematical Physics Degree and I'm thinking about a project to do over the summer.

First mistake... you spend too much time in the house. Go outside and play.

Agreed Go play.

"Modeling" has one 'd'... even if you're talking about FEM/ flow analysis etc.

[riggerrob 643]

PM Dr. Kallend, Winsor or BillVon with a hyperlink to this thread so they can all take a peek at it.

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Nice pun!
Gary Peek is into that sort of mathematical modelling stuff.

[riggerrob 643]

Wing-suiters can provide volumes of GPS and Pro-Track (fancy recording altimeters) data.

[Unparagoned 0]

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I've finished my second year of my Mathematical Physics Degree and I'm thinking about a project to do over the summer.

First mistake... you spend too much time in the house. Go outside and play.

PM Dr. Kallend, Winsor or BillVon with a hyperlink to this thread so they can all take a peek at it. I'm sure out of all of them, you're bound to get some guidance.

Well I won't be skydiving much during the summer and won't be until I get back to uni, so I was thinking if the project goes well I can use it as one of the projects for the 3rd or 4th year, giving me more time to skydive instead of doing work.

I want this to be mainly thoeretical with maybe some cross referencing to reality now and then, I don't want it to be practicle.

Wingsuit data isn't going to be much help at all because it gives no information at all on the angle the person is at. Maybe if I find someone with gps and stuff I can get them to try different positions or so to test the results...

[Unparagoned 0]

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How about using a number of rectangular blocks in a wind tunnel/computer model?

Use one large block for the body and 4 smaller blocks representing the legs.

Simply model the lift/drag etc of the blocks arranged in an almost straight line (as in during a conventional track) then model the lift/drag etc of the blocks arranged in an atmonauti position.

Because they're blocks you still produce figures you can work with (I presume) but you're also producing results which should broadly mirror those which you might expect in real flight.

Then repeat at different angles etc and find the best for each. A comparison of the results of the best position obtained from each should show which is "better" - atmonauti or tracking.

That sounds like a good idea but I want to keep it simple first, if I just use a single block at first, to get in the right area. Going straight into having various blocks complicates matters greatly and considering it is a complicated topic to start with it is not practical for me to try. Although if the model works I can make it more complicated like you suggest.

[mr2mk1g 10]

If you do decide to make the project more complicated I've modified my idea to make it more simple.

Go with three blocks and lay them out like the wings on an F14. Central block stays in the same position (body). Two smaller blocks can be in either a swept back position or stuck out from the sides at an angle.

You could probably even find data on and/or an explanation of the theory behind the F14 wings and apply it to the data you have regarding a tracking/atmonauti skydiver... if you were to make it more complicated of course.

[billvon 3,080]

I'd keep it simple.

Drive is easy. It's the cosine of the angle of flight times weight.

For lift you have L = Cl * De * (V^2/2) * A

Where Cl is the coefficient of lift, De is the density of air, V is speed and A is wing area.

For parasitic drag you have D = Cd * De * (V^2/2) * A

Where is Cd is the coefficient of drag, De is density of air (rho) V is speed and A is frontal area. Look familiar?

You may want to break out induced drag separately, since a tracker is sorta like a wing. Parasitic drag is the drag from the roughness of the fabric, the work you do compressing the air on all sides of you etc. while induced drag is an unavoidable consequence of lift. Formula is similar.

Note that some people break drag out into three parts - induced (due to lift) form (due to moving the air out of the way) and friction. You can do that too if you want.

In all cases, it's figuring out the coefficients that's tricky, since they depend on angle of attack, shape of the wing etc. I'll leave that as an exercise for the reader, but one hint is that you can assume that Cl has a linear relationship to AOA at small angles of attack (well below stall.) A good way to approach it would be to assume stable flight (so everything balances) and then see what a change in angle of attack does to glide ratio, which should be computable via figuring out required drive.

[MakeItHappen 15]

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Hi, I've finished my second year of my Mathematical Physics Degree and I'm thinking about a project to do over the summer. I was thinking about trying to do a very basic model of when someone is tracking. I've seen here some people say that in the atmonauti angle you can track further than in a flat track, and others say the opposite. Even then if one side is right, which angle to the horizontal do you want to track at, 1, 5, 15 degrees? The steeper the angle you get more drive and travel faster but you reduced lift and vice versa. Also the faster you go the more drag you get, etc. I doubt it is possible to do this analytically so I would be solving it using c++. On the physics side I plan on simply using newtonian physics to calculate lift and drive, and use some drag formulas for the drag for the relative wind direction...
I've only briefly gone through the idea and it may change dramatically. I doubt I will be able to get data that is useful quantitatively but you should be able to get some qualitative information which could be useful. e.g. 7 degree to the horizontal is the idea track position(assuming you are a solid rectangular sheet :P) Even if it doesn't give any useful results it will be a nice exercise for me.

Has anyone done anything like this before? Are there any useful libraries dealing with fluid flow that could make it much easier to do? What do you guys think overall, is it a waste of time, should I do it on something else?

There are a few ways to approach this.
You can do a vortex lattice distributed along surfaces with vortex shedding, aka computational fluid dynamics. This might be beyond your education right now, although the equations for computational fluid dynamics are very similar to electrical charge distributions.
see "Vortex Lattice Theory Applied to Parachute Canopy Configurations" by Jan Meyer and Jim Purvis, AIAA 8th Aerodynamic Decelerator and Balloon Technology Conference, 1984

A simpler, and potentially more useful, thing to do is to calculate the trajectory when changing from an initial configuration to a final configuration. Say state 1 is flat fly or head down or sitfly. Then at t=0 you change into state 2 that represents a track. Then provide the answer of what the trajectory is. Useful info from this would be separation distance, altitude lost and velocity versus time.

You can parametrically represent Cl and Cd as step functions, linear functions or whatever your heart desires.

A simple numerical method to update positions, velocities and accelerations is to use the constant acceleration equations of motion for very small time intervals. We used this in a line-sail code and several other parachute simulations at Sandia Labs.
I can't find the reference for this one, but I think it is referenced in the AGARD report below. Line sail is the same phenomena that jumpers call line dump. Plus I am currently using this method to model swoop trajectories.

See also
AGARD-AG-319
Design and Testing of High-Performance Parachutes

A tiny project I did one summer, in addition to my regular work for Sandia, was "Average Landing Force Dependence on Length and Direction of Landing, Parachute Velocity Components and Wind Speed." by Jan Meyer, AIAA 9th Aerodynamic Decelerator and Balloon Technology Conference, 1986

There are also some 'simple' mid-air retrieval systems that you can model easily. This is outside of skydiving, but it may work for a little project. Or you could adapt it to catching a cutaway canopy and show how dangerous that can potentially be. But we already know that - so what's the point?

Other little projects may also upgrade these:
How Far does a Jumper Fall After Pulling?
Collision Course
What Determines fall Rate?

Keep in mind that most analyses like this will be lost on the average jumper. They want to know body positions at point A and point B. For that, you'd need wind tunnel experiments.

If you want more info, please contact me directly. Follow the link in the footer for contact info.

.

.
Make It Happen
Parachute History
DiveMaker

[Unparagoned 0]

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I'd keep it simple.

Drive is easy. It's the cosine of the angle of flight times weight.

For lift you have L = Cl * De * (V^2/2) * A

Where Cl is the coefficient of lift, De is the density of air, V is speed and A is wing area.

For parasitic drag you have D = Cd * De * (V^2/2) * A

Where is Cd is the coefficient of drag, De is density of air (rho) V is speed and A is frontal area. Look familiar?

You may want to break out induced drag separately, since a tracker is sorta like a wing. Parasitic drag is the drag from the roughness of the fabric, the work you do compressing the air on all sides of you etc. while induced drag is an unavoidable consequence of lift. Formula is similar.

Note that some people break drag out into three parts - induced (due to lift) form (due to moving the air out of the way) and friction. You can do that too if you want.

In all cases, it's figuring out the coefficients that's tricky, since they depend on angle of attack, shape of the wing etc. I'll leave that as an exercise for the reader, but one hint is that you can assume that Cl has a linear relationship to AOA at small angles of attack (well below stall.) A good way to approach it would be to assume stable flight (so everything balances) and then see what a change in angle of attack does to glide ratio, which should be computable via figuring out required drive.

Thanks, I don't have time atm to go through your advise in detail atm, but I get the sort of gist. Your answer seems kind of text book, but I was hoping to analyse the drive and lift through newtonian mechanics, i.e perfectly elastic collisions between air and the body, so all the lift and drive will be calculated through conservation of momentum, and maybe an added parasitic drag as some kind of error term or something. It would have to be on a computer because the faster the different angle of the realative wind hits you, etc it all feeds back into each other. e.g. The instantanious drive of someone traveling at 1:1 at an angle of 45 degrees is zero.

Also the angle of flight is what we want to find out, that is the whole aim of the project. To clarify, angle of flight to me means the angle of the trajectory of the person through the sky. The angle of flight is not the angle of the person relative to the horizontal.

[Unparagoned 0]

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A simpler, and potentially more useful, thing to do is to calculate the trajectory when changing from an initial configuration to a final configuration. Say state 1 is flat fly or head down or sitfly. Then at t=0 you change into state 2 that represents a track. Then provide the answer of what the trajectory is. Useful info from this would be separation distance, altitude lost and velocity versus time.

You can parametrically represent Cl and Cd as step functions, linear functions or whatever your heart desires.

A simple numerical method to update positions, velocities and accelerations is to use the constant acceleration equations of motion for very small time intervals. We used this in a line-sail code and several other parachute simulations at Sandia Labs.
I can't find the reference for this one, but I think it is referenced in the AGARD report below. Line sail is the same phenomena that jumpers call line dump. Plus I am currently using this method to model swoop trajectories.

Keep in mind that most analyses like this will be lost on the average jumper. They want to know body positions at point A and point B. For that, you'd need wind tunnel experiments.

If you want more info, please contact me directly. Follow the link in the footer for contact info.
.

This is the track I was going to go down, derive some "simple" equations and then use the computer to update in small time periods. I've done a course which covered modelling PDEs which is essentially what I want to do. Derive PDEs useing newtonian mechanics, and then solve them numerically. So at least I know the way I wanted to solve them is on the right track. I felt the analysis could be useful to the common jumper. I worked out that the initial drive right at the start of the track is optimal at 45 degrees, if that turns out as true for the first 5 seconds then it could be useful information. Also you see on these boards many people talking about how jumpers track down from a formation, the analysis could simply show that they are infact just tracking faster(faster means they have the same trajectory but obviously they will be further down than others) and angles and whatever explains why although they apear to be tracking down and steep, they are tracking faster and on the same trajectory as others... or whatever

[kallend 2,112]

IMO airflow over a human body is far more difficult to model than, say, an airplane. I'm not sure even CFD codes will handle it unless oversimplified to a ridiculous extent. There's a very good reason research wind tunnels are built at great expense - there's only so much you can do without doing an actual test.

...

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

[billvon 3,080]

>Your answer seems kind of text book, but I was hoping to analyse the
> drive and lift through newtonian mechanics, i.e perfectly elastic collisions
> between air and the body, so all the lift and drive will be calculated
> through conservation of momentum . . .

For that to work you'd have to be able to do FEA at an impossibly fine grain; it would take an awful lot of computing power. Tracking momentum transfer between gas molecules moving in a Brownian fashion is not easy.

>It would have to be on a computer because the faster the different angle
>of the realative wind hits you, etc it all feeds back into each other. e.g.

Well, a spreadsheet would do it. You just have to iterate a lot.

>The instantanious drive of someone traveling at 1:1 at an angle of 45
>degrees is zero.

?? The instantaneous acceleration of anyone in stabilized fall/flight is zero in all dimensions, no matter what they're doing. We usually refer to forward speed as 'drive' which is definitely not zero in a tracker.

>Also the angle of flight is what we want to find out, that is the whole aim
>of the project. To clarify, angle of flight to me means the angle of the
>trajectory of the person through the sky. The angle of flight is not the
>ngle of the person relative to the horizontal.

The two angles are the same in still air. There's also the angle of attack, which is the angle between the jumper's wing and the relative wind. Then there's angle of incidence, which is the angle between the jumper's trajectory and the wing.

To figure out the various angles, you have to use both trigonometry and lift/drag equations. You can stick various numbers into the lift and drag equations until you get something that comes close to balancing. Then iterate around a few variables - angle of attack, airspeed, glide slope - and see what gives you a stable flight result. Once you know angle of attack and drive required, you can calculate what sort of glideslope and speed you will require to maintain that.

[JohnRich 4]

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Mathematical Physics Degree...a very basic model of when someone is tracking.

Darn! I was hoping this was going to be a thread full of photos of hot babes modeling skydiving gear. Dang dang dang!

Math - blech!

[Avion 0]

Regarding the flight angle, the goal of Atmonauti is to fly parallel headfirst or feet first in to the relative wind. That particular angle will depend on, among other things: Body weight, cross-sectional surface area, and how much vertical lift the atmonaut is able to generate by arching.

I also believe the goal is to maximize flight time rather than horizontal distance.

Cheers

[Avion 0]

How about using polygon modeling, such as modern 3D game engines use, then compute totals using the individual values determined for each polygonal surface.

I expect the results would be accurate enough to get a viable model, or at least be a good place to start. I wonder how much the actual performance of the whole model would diverge from the predicted performance of the sum of its parts. I suppose that answer will have to wait until both abstract, software, and physical, wind tunnel, models are made and tested.

Cheers

[tso-d_chris 0]

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Note that some people break drag out into three parts - induced (due to lift) form (due to moving the air out of the way) and friction.

I learned the three types were:

Profile drag, due to the viscosity of the air as it passes over the surface of the wing.

Induced drag, which is the horizontal component of the Total Aerodynamic Force, which is perpindicular to the chord line. Use of the term drag would imply that Induced drag can only exist with a positive angle of attack.

Parasitic drag is drag due to non lift producing parts such as your canopy lines or the jumper under the canopy.

Part of the problem with modeling a track mathematically is that few people are able to track with a low enough angle of attack to keep from being well into stall range, and the movement due to deflection is going to change drastically with slightly different tracking positions between jumpers.

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[tso-d_chris 0]

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the goal of Atmonauti is to fly parallel headfirst or feet first in to the relative wind.

Jimmy Tranter and The Freedom Of Flight School did a lot of feet first tracking. He called it the MoonSlide. Nobody around here had seen anything like it before. This was a couple years ago, and those guys could track flatter feet first than 98% or more skydivers can track headfirst. The training tapes were very impressive to watch.

For Great Deals on Gear

[Unparagoned 0]

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>Your answer seems kind of text book, but I was hoping to analyse the
> drive and lift through newtonian mechanics, i.e perfectly elastic collisions
> between air and the body, so all the lift and drive will be calculated
> through conservation of momentum . . .

For that to work you'd have to be able to do FEA at an impossibly fine grain; it would take an awful lot of computing power. Tracking momentum transfer between gas molecules moving in a Brownian fashion is not easy.

>It would have to be on a computer because the faster the different angle
>of the realative wind hits you, etc it all feeds back into each other. e.g.

Well, a spreadsheet would do it. You just have to iterate a lot.

>The instantanious drive of someone traveling at 1:1 at an angle of 45
>degrees is zero.

?? The instantaneous acceleration of anyone in stabilized fall/flight is zero in all dimensions, no matter what they're doing. We usually refer to forward speed as 'drive' which is definitely not zero in a tracker.

The acceleration of someone may be zero but their drive may not be zero, as you have to factor in drag. e.g. acceleration at terminal velocity is 0, but weight is not zero. I mean drive as in a force not speed.

[Unparagoned 0]

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>Your answer seems kind of text book, but I was hoping to analyse the
> drive and lift through newtonian mechanics, i.e perfectly elastic collisions
> between air and the body, so all the lift and drive will be calculated
> through conservation of momentum . . .

For that to work you'd have to be able to do FEA at an impossibly fine grain; it would take an awful lot of computing power. Tracking momentum transfer between gas molecules moving in a Brownian fashion is not easy.

I was planing on assuming a laninar ariflow.. and just use say desnsity of the air, velocity, and surface area, and angle to the relative wind to find the change in momentum. Keeping it simple, sticking in some co-efficients you can get in the right range for terminal velocity of a skydiver. This is why I'm not going to consider complicated shapes to start with, just a single block. Anyway I'll go through my plan in more detail whenever the weather is bad :P (it shouldn't be too long as I live in england)