Wingloading/Density Altitude Equation

[CanuckInUSA 0]

I'm wondering if guys like BillVon or Kallend (or anyone else) has come up with an equation that factors in wingload and density altitude.

You see the other day I was doing a little Ground Launching with some friends here in Colorado (launching from 6800 MSL with a density altitude likely somewhere likely close to 9000 feet, maybe more) and my Samurai 136 loaded at 1.3:1 did not perform nearly as well as the lesser experienced guys who were flying lighter loaded canopies.

So do you guys have an equation that might work? I know the California Ground Launching guys say they've seen the best performance in the 1.3 - 1.4 wingloading. But due to our higher density altitude I'm thinking that 1.0 - 1.1 might be better. But an equation to convert their WL/DA to our DA might be better than just making a blanket guessing statement like I just did thinking that 1.1 would be better here.

Make sense or am I just rambling ... again ...

Try not to worry about the things you have no control over

[CanuckInUSA 0]

Dude break out your Grade 9 Algebra text right? Dude ... who are you talking to? You you moron ... oh, okay just making sure ...

Anyone else? Bueller?

Try not to worry about the things you have no control over

[f1shlips 2]

Quote

has come up with an equation that factors in wingload and density altitude.

Since this thread is going nowhere.

I have one:

b = Wl + Da / Be;


That's the number of (whole) burritos you can consume given a certain wingloading and a certain density altitude after consuming a certain quantity of beers.

I'm sure someone will argue with me about it.

--
drop zone (drop'zone) n. An incestuous sesspool of broken people. -- Attributed to a whuffo girlfriend.

[billvon 3,111]

Density = (Pd / (Rd*T)) + (Pv / (Rv*T))

where D = density, Pd = pressure of dry air, Pv= pressure of water vapor, Rd = gas constant for dry air, Rv = gas constant for water vapor, T = temperature (K)

But that doesn't help much, does it.

I think you want a number that says "if you go up X feet you must change your canopy size Y percent" and I don't think such a formula exists. Too many things change. Check out this page:

http://aero.stanford.edu/StdAtm.html

This lets you enter altitudes and see what changes (pressure etc.)

[MakeItHappen 15]

Quote

But an equation to convert their WL/DA to our DA might be better than just making a blanket guessing statement like I just did thinking that 1.1 would be better here.

I do not have 'an equation' that you could empirically adjust for DA, but I do have these plots you can use to see the effects.

The trajectory is only for the natural recovery part of a swoop, given the initial conditions. The initial conditions would be the result of a speed inducing maneuver. Riser or toggle inputs change the trajectory of course. That is not modeled (yet). The trajectories (z vs t and x vs z plots) go to a straight line after 6 or seven seconds. That represents the steady state descent. In real life you do the flare before that to finish off a swoop landing.

The z vs t shows that you lose more altitude as DA increases. That should not be a surprise to you.

The x vs z shows that the trajectory gets 'stretched' in both the x and z directions as DA increases.

The a vs t shows that accelerations are lower at higher DA. That means the 'feel' you have through the harness will be different. May be that realization will allow you to adjust properly.

There are several WLs on each plot.

This was just data I had on hand for swoop landings, not slope soaring. Effects for 9k DA would be larger of course.
You should be able to see the trends with these plots.

I will also note that your guess of lower WLs at higher DA is supported by these plots.
Compare the WL=1.6 at DA=0 to WL=1.4 at DA=5k on all of the plots. They seem to be similar trajectories. IOW, for this specific case, a WL=1.6 and DA=0 is about the same as a WL=1.4 and DA=5k.
Compare the pink line on DA=0 to the blue line on DA=5.

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Make It Happen
Parachute History
DiveMaker

[MakeItHappen 15]

I overlayed the two scenarios of:
1: DA = 0, WL = 1.6 (black line)
2: DA = 5, WL = 1.4 (red line)

You can see that they are almost identical.

Normally, you only vary one parameter at a time, so I had to adjust the legends to show the two cases properly.

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Make It Happen
Parachute History
DiveMaker

[MakeItHappen 15]

OK I do have an empirical equation that you can use:

WL(2) = [rho(2)/rho(1)] * WL(1)

rho = density at a density altitude
WL = wing loading

Example 1:
point 1 = sea level
point 2 = 5 k DA
rho(1) = 0.00237689; // slugs/cubic feet, sea level
rho(2) = 0.00204817; // slugs/cubic feet, 5K
WL(1) = 1.3
=>
WL(2) = 1.12

IOW, if you want the same performance of a 1.3 WL at SL, at 5K DA, then use a WL of 1.12, everything else being constant.

Example 2:
point 1 = sea level
point 2 = 8 k DA
rho(1) = 0.00237689; // slugs/cubic feet, sea level
rho(2) = 0.00186845; // slugs/cubic feet, 8K
WL(1) = 1.3
=>
WL(2) = 1.02

IOW, if you want the same performance of a 1.3 WL at SL, at 8K DA, then use a WL of 1.02, everything else being constant.

I'll leave it as an exercise for others to look up densities at other altitudes.

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Make It Happen
Parachute History
DiveMaker

[firstime 0]

have to add this to my ep's on my next jump

[CanuckInUSA 0]

Quote

I think you want a number that says "if you go up X feet you must change your canopy size Y percent"

When I started this thread, I was first being lazy wanting a quick answer (and some of you gave me a headache with your responses). But it's is an interesting topic. Not that I have all these CO Ground launching exit points, but what obviously works at one DA will not work at another. It's all making sense now why the performance for myself got worse as the afternoon worn on. It wasn't me, my canopy was too small for the DA I was at. And we really weren't all that high when it comes to potential launch sites here in Colorado. Hmmm ... shit ... anyone want to trade a Samurai 136 for something similar but bigger?

Try not to worry about the things you have no control over

[mjosparky 4]

My head hurt, I am going to go lay down now.

Sparky

My idea of a fair fight is clubbing baby seals

[quade 4]

Jan --

I recall you once telling me that I should keep my explainations simple because skydivers can't do math.

Anyway, that's the way I remember it.

And I believe you're correct about it too.

As a flight instructor I had to know all sorts of crap, but when it came to actually flying I used rules of thumb that were "close enough". Years ago I wrote a web page to try to simplify the concept of Density Altitude so it wasn't just understandable, but actually usable with simple rules of thumb.

http://www.futurecam.com/densityAltitude.html

While this doesn't -exactly- address the issue of what canopy to use at what density altitude, it should give a person a rough idea that as density altitude goes up, the wingloading should probably go down to maintain roughly the same performance figures. How much? Roughly 2% increase in area per 1000 feet difference, compounded.

If you jumped a 150^2ft canopy at sea level on a standard day, then for a 5000 foot difference in DA you'd want to jump about a 166^2ft canopy. (((((150*1.02)*1.02)*1.02)*1.02)*1.02)

At least, that's the way I have it figured.

That said, I would be remiss in my duties if I didn't also mention that (obligatory comment about all other things being equal and within reason) glide slope is independant of wingload. What I mean my this is that if you where trying to match the slope of the hill, it should not matter what your wingloading is since that is not what controls the glide slope, only the speed at which you travel down it.

(again all things being equal and within reason) To change the angle of the glide slope, you'd need to change the angle of attack of the wing.

quade -
The World's Most Boring Skydiver

[kallend 2,146]

Quote

Jan --

I recall you once telling me that I should keep my explainations simple because skydivers can't do math.

That's a bit of an over-generalization. I know 5 4 6 some skydivers that can do math.

...

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

[murps2000 86]

That is way cool. You just mathematically demonstrated the answer to a question often needed to be answered by trial and error. Thank you, and thanks to C. in U.S.A. for asking the question.

So in order to fly the same as my 2:1 canopy at sea level, I'd need something loaded 1.72:1 at 5K, and 1.57:1 at 8K, assuming the same model parachute, of course. That's a bigger difference than I thought it would be.

Do you have reference to a chart that lists slugs/cubic feet (air mass, correct?) for different density altitudes?

[MakeItHappen 15]

Quote

That is way cool. You just mathematically demonstrated the answer to a question often needed to be answered by trial and error. Thank you, and thanks to C. in U.S.A. for asking the question.

So in order to fly the same as my 2:1 canopy at sea level, I'd need something loaded 1.72:1 at 5K, and 1.57:1 at 8K, assuming the same model parachute, of course. That's a bigger difference than I thought it would be.

Do you have reference to a chart that lists slugs/cubic feet (air mass, correct?) for different density altitudes?

Thanks!

Calculator Converter between DA & WL

Hope this works for all the jumpers that can't do math.
I'll prissy it up with more DAs and navigation.

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Make It Happen
Parachute History
DiveMaker

[murps2000 86]

Thanks!

Calculator Converter between DA & WL

Hope this works for all the jumpers that can't do math.
I'll prissy it up with more DAs and navigation.


No, thank you. That was slick. Quantified the answer to one of my undying questions for the past 5 years.