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outrager

Real life L/D challenge at Eiger

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With 2m 50s flights from the higher exit, a 20mph tailwind gives a free mile of distance, while the same headwind takes it from you. For such long flights, wind can be used creatively to do flights that would otherwise be impossible to do.

As can be seen from Wingsuit Studio simulations, longer (slower) flights allow lower L/D threshold to achieve the same goal compared to faster flights.Yuri


For those of us who don't have similar wingloading, I don't see the balloon technique (grabbing the biggest column of air and waiting for the wind to come to by) working so well.. ?
"The evil of the world is made possible by nothing but the sanction you give it. " -John Galt from Atlas Shrugged, 1957

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one famous know jumper already flew to grindewald few years ago, but he not say much. Not like this shit you can read on Matt website.
"i was..., i was,...", "only american suit jumping there,...." all this bullshit ! and we can not even see on video the entire flight from the high exit. Fog hmmmmm ! nice after effects :o)
what can we see on GPS track, opening happend before the real bottom of the valley
but congrat to Dean, the one who open the exit and don"t post vantard stuff

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Maria, there's nothing a little PFM cannot do. ;)

The question is like this: if a jumper has sustained speeds [normalized to sea level and standard temperature of 15C/59F] in a contemporary wingsuit of Vxs = 75mph, Vys = 30mph (L/D = 2.5), and he's given some magic wingsuit with L/D = 4.5 (an improvement by factor of 4.5/2.5=1.8, or 80%), how would his horizontal & vertical sustained speeds be affected? Would his vertical speed be about the same and horizontal speed be 1.8x faster, or horizontal speed be about the same and vertical speed be 1.8x slower, or somewhere in between, or what?

It turns out we can answer this question precisely if we know where this improvement mostly comes from: is coefficient of lift 1.8x higher and drag is about the same, or lift is about the same and drag is 1.8x lower, or the improvement is split in half by increase in lift and reduction in drag?

From Wingsuit Equations, the magic lift and drag coefficients are related to sustained horizontal and vertical speeds as:



Kl = Vxs/Vs^3, Kd = Vys/Vs^3


where Vs = (Vxs^2 + Vys^2)^0.5 is total sustained speed. (See Derivation tab in WSE module in Wingsuit Studio.)

Reversing these equations, we get sustained speeds:



Vxs = Kl*(Kl^2 + Kd^2)^(-0.75)
Vys = Kd*(Kl^2 + Kd^2)^(-0.75)


Omitting some simple algebra, the ratio of sustained speeds of suits 1 and 2 is:



Vxs2/Vxs2 = (Kd1/Kd2)^0.5*(((L2/D2)^2 + 1)/((L1/D1)^2 + 1))^(-0.75)*((L2/D2)/(L1/D1))
Vys2/Vys2 = (Kd1/Kd2)^0.5*(((L2/D2)^2 + 1)/((L1/D1)^2 + 1))^(-0.75)


where L1/D1 and L2/D2 are L/D's of the 1st and 2nd suit, respectively.

So in this case we have L1/D1 = 2.5, L2/D2 = 4.5.

Scenario 1: improvement from 2.5 to 4.5 came from 1.8x reduction in drag, so Kd1/Kd2 = 1.8.



Vxs2/Vxs2 = 1.8^0.5*((4.5^2 + 1)/(2.5^2 + 1))^(-0.75)*(4.5/2.5) = 1.08
Vys2/Vys2 = 1.8^0.5*((4.5^2 + 1)/(2.5^2 + 1))^(-0.75) = 0.60


In this case, horizontal speed of the 4.5 suit will be 8% faster while vertical speed will be 40% slower:

75mph/30mph becomes 81mph/18mph

-------

Scenario 2: improvement from 2.5 to 4.5 came from 1.8x increase in lift, so Kd1/Kd2 = 1.



Vxs2/Vxs2 = 1^0.5*((4.5^2 + 1)/(2.5^2 + 1))^(-0.75)*(4.5/2.5) = 0.80
Vys2/Vys2 = 1^0.5*((4.5^2 + 1)/(2.5^2 + 1))^(-0.75) = 0.45


In this case, horizontal speed of the 4.5 suit will be 20% SLOWER while vertical speed will be 55% slower:

75mph/30mph becomes 60mph/13.4mph

-------

Scenario 3: improvement from 2.5 to 4.5 came from 1.34x increase in lift and 1.34x reduction in drag (1.34*1.34=1.8), so Kd1/Kd2 = 1.34.



Vxs2/Vxs2 = 1.34^0.5*((4.5^2 + 1)/(2.5^2 + 1))^(-0.75)*(4.5/2.5) = 0.93
Vys2/Vys2 = 1.34^0.5*((4.5^2 + 1)/(2.5^2 + 1))^(-0.75) = 0.52


In this case, horizontal speed of the 4.5 suit will be 7% SLOWER while vertical speed will be 48% slower:

75mph/30mph becomes 70mph/15.6mph


While examples are hypothetical, they give an idea how changes in lift and drag affect horizontal and vertical speeds: we see that the strongest effect of wingsuit improvement is on fallrate, not horizontal speed.

It's magic... pure fucking magic! ;)

Yuri
Android+Wear/iOS/Windows apps:
L/D Vario, Smart Altimeter, Rockdrop Pro, Wingsuit FAP
iOS only: L/D Magic
Windows only: WS Studio

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Tony, you can estimate how your balloon technique will affect your trajectory on a b a s e jump compared to your max L/D mode by measuring sustained horizontal and vertical speeds with GPS on a skydive and plugging the numbers in Wingsuit Studio. You can even run a virtual race between the two techniques in World BASE Race module. :)
Android+Wear/iOS/Windows apps:
L/D Vario, Smart Altimeter, Rockdrop Pro, Wingsuit FAP
iOS only: L/D Magic
Windows only: WS Studio

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Yuri,

Something I've never understood, but perhaps you can explain, is how is energy maintained with decreasing fall rates? I'm talking about sustained flight, not just flares.

Gravity is our engine, right? By the design of the wings, and the angle of our bodies, we're re-directing downward energy (generated by falling) into forward movement. The faster we fall, the faster we can go forward, correct? Isn't this why heavy guys, with the same surface area and at the same glide ratio, will fly faster forward (but also eat up altitude)?

So as the lift (or whatever it is) generated by our suits begins to significantly slow down our fallrate, what keeps us going forward? Isn't there a point where the decrease in our fallrate results in such a significant decrease in energy that we can no longer go forward with enough velocity to generate lift (stall)?

Is there a theoretical limit to fallrate where sufficient forward speed can longer be maintained?

Sorry if I'm not expressing this question well enough.

Edited to add:
I guess what I'm trying to say is that if I my terminal velocity was 15.6mph so that when I jump from a cliff, I only accelerate up that point, would I really go 70mph forward? How? Where did that energy come from? I suppose my question is revealing an admittedly ignorant misunderstanding of this issue. A factor of 70mph/15.6mph doesn't really indicate a terminal velocity of 15.6, but of some number in between, correct? A lil' help for us math challenged folk?
Brian Drake

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Brian,

Think about high-performance gliders: they have ridiculously low sustained rates of descent - 1mph or so with forward speed of ~70mph at best L/D. Where do they take all this energy to propel themselves a hundred feet forward every second while going down a mere 1.5ft in the same second? They do it by minimizing drag as much as possible. At L/D = 70, a 700lbs glider with giant wings has only about 10lbs of drag. So 700lbs over the distance of 1.5ft down generates the same amount of energy as amount spent dragging 10lbs for 105ft horizontally. (700*1.5 = 10*105)

So, to answer your question, the energy is maintained with decreasing fall rates by spending it on drag at a lesser rate.

If you're interested how the trajectory of a BASEjump with 70/15.6mph would look like, here's a simulated jump from High Nose - you'll be pulling over Horner Pub at comfortable 400ft after 51s flight, with the added bonus of actually going UP 50ft for about 5 seconds without any effort. ;)

Yuri
Android+Wear/iOS/Windows apps:
L/D Vario, Smart Altimeter, Rockdrop Pro, Wingsuit FAP
iOS only: L/D Magic
Windows only: WS Studio

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Typo:



Vxs2/Vxs1 = (Kd1/Kd2)^0.5*(((L2/D2)^2 + 1)/((L1/D1)^2 + 1))^(-0.75)*((L2/D2)/(L1/D1))
Vys2/Vys1 = (Kd1/Kd2)^0.5*(((L2/D2)^2 + 1)/((L1/D1)^2 + 1))^(-0.75)

Android+Wear/iOS/Windows apps:
L/D Vario, Smart Altimeter, Rockdrop Pro, Wingsuit FAP
iOS only: L/D Magic
Windows only: WS Studio

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Gnarly equations Yuri, thanks. Ren alerted me to this thread, I didn't know it was happening.
A couple clarifications: I never said or meant to even imply that I was the first to fly to the valley at grindelwald!

Dean Potter jumped the Eiger 27 times just this year! (sidenote: Andy West has also jumped it 28 times just this year and 43 times in his life, probably a record).

I know that Dean pulled over flat fields in the same place as me (at the camping) a least 4 times. I don't want to speak for Dean but I'm sure that neither of us thought we were the first, in fact we were sure that many other better wingsuit pilots had already done it, years ago.

Honestly I'm sure that Julian Boulle can fly to Grindelwald on his back, he's better than we'll probably ever be. And there are several other wingsuit pilots that we really look up to who could fly further, and who probably aren't looking at this forum either.

Anyway it's too bad the season is coming to an end, we were just starting to have fun but now the snow is getting deep already. Here's video from friday, nothing smashing just a fun flight. http://www.vimeo.com/7103784

Have fun everyone.

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Thank you Yuri for that comprehensive reply. The significance I see is that there are options when designing for improved glide. You can opt for design that is biased toward very slow vertical speed, as for your scenario 1, sacrificing forward speed. This is consistent with the fact that wing area will have to be that much bigger, and we can therefore expect drag to be higher. Alternatively, you design to achieve speeds that you mentioned in Scenario 3, where you balance increase in lift and reduce drag to keep forward speed relatively high.
I am contributing to an article for The New Scientist magazine on - you guessed it- landing a wingsuit without a parachute. It is essential to my concept that the glide of the wingsuit can be sustained at between 1:4-5 , and that there is a slight reduction in horizontal speed . My maths is terrible but you have confirmed that speeds in both directions can be reduced. Would you mind if i direct the author of the article to your PFM laboratory?

(pronounced G - jii is the force that makes you fly!)

Jii-Wings - no strings!

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we see that the strongest effect of wingsuit improvement is on fallrate, not horizontal speed.



Correct, Yuri! Maybe the easier way to show it for "non-number" public is graphical explosure (e.g. Polar).

In my opinion:
1) the improving of the horizontal speed for wingsuit technique in large-scale is no more possible (without an engine).
2) for reducing of drag we can use new materials only. Body position (wings geometry) is our limit here.
3) increasing of the lift is the way for upcoming wingsuit models. New aerodynamic solutions are here in demand!

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