0

# Glide ratio for different canopies

## Recommended Posts

Nicely stated Yuri! I hadn't tried to run those numbers.

An extreme example of what Yuri's talking about is seen in those videos of tiny non-landed canopies, maybe 21 or 25 square feet ... where the jumper looks like he's face down about 45 degrees off the vertical because of all his body drag, no matter how efficient the wing might be.

But Yuri's point is that this sort of thing has a significant and variable effect for "normal" fast canopies too.

##### Share on other sites
Interesting stuff. This means that vidiots wanting to get back from a long spot after a tandem vid have a lot better chance if they unclip those big wings on their video suits.
Dave

Fallschirmsport Marl

##### Share on other sites
Quote

so in non-math terms...

At full speed, the drag of the human is more. The drag "moves" the human back in the "window", changing the angle of attack of the canopy to be more "divey". With the "divey angle of attack", the speed of the canopy increases, causing even more drag, causing even more shift of the window, changing the angle of attack even more - until a fast divey equilibrium is found...

In deep brakes, the drag of the human is less. The lack of drag "moves" the human forward in the "window", changing the angle of attack of the canopy to be "flat". With the "flat angle of attack", the speed of the canopy decreases, causing even less drag, causing even more shift of the window, changing the angle of attack even more - until a slow flat equilibrium is found.

Is this accurate in your opinion?

Now there is something seriously wrong...
Did you think before posting that..

In any normal situation the canopy makes more drag than the body (except maybe Luigi if he gets an even smaller wing..), and when the speed increases, increases also drag of the canopy. And because it has more drag, it increases faster than the drag of the body. For example, if the drag of the canopy is 4 and drag of the body is 2, when the speed doubles, the drag of the canopy is 16 and the drag of the body is 4. This means that when the speed increases the body under the canopy is shifted forward making the canopy less divey. This is why the canopy wants to level out at the end of the swoop, and its harder to keep the canopy diving when the speed increases. I wouldn't want to swoop a canopy that gets more divey as the speed increases...

I'm not sure about this but I think theres also a problem with Yuri's calculations. When the speed decreases from 46mph to 25mph, it reduces the drag of the canopy too. So IMHO you can't use that 28% in the slower speed calculations..

##### Share on other sites
God, that post is old. I had to refresh my memory.

If you see my last line, I asked, "is that accurate of your opinion?"

I never said I believed what I wrote. I was just trying to convert math to descriptions.

I agree it may be flawed.

##### Share on other sites
Wetswooper wrote:

Quote

Did you think before posting that..
[…]
For example, if the drag of the canopy is 4 and drag of the body is 2, when the speed doubles, the drag of the canopy is 16 and the drag of the body is 4. This means that when the speed increases the body under the canopy is shifted forward making the canopy less divey. This is why the canopy wants to level out at the end of the swoop, and its harder to keep the canopy diving when the speed increases.

Jeez, you almost had me there for a moment!

You learned something wrong about how drag works. It's almost a subtle change of wording but makes all the difference:

WRONG:
Drag is squared when speed doubles.

RIGHT:
Drag increases with the square of speed.

(Technically not perfectly 100.000% true, but still a very very useful aerodynamics rule.)

So if you have two objects with drag 4 and 2 (like you described, a 2:1 ratio), if the speed doubles you get:

WRONG: square each to get 16 and 4, which is now a 4 to 1 ratio

RIGHT: speed doubles, so the drag increases by 2 to the power 2 = 4
So the drags become 4*4= 16, and 2*4= 8, which is still a 2 to 1 ratio.

Speed therefore doesn't change the inherent balance between the drag of two objects, so no matter where they are acting as a lever on each other, things won't go out of balance as the speed changes.

It all reminds me of Galileo's thought experiment about falling objects connected or not connected by string, for the situation you described would cause some weird effects. Small items would become far less draggy than large items at high speed, and since lift behaves in the same way as drag relative to speed, airplane tails (smaller than wings) would soon lose their effectiveness in countering negative pitching moments of normal airfoils and cause aircraft to nose over and crash.

Hope that helps.

What I've written should get rid of the idea that a canopy would pitch up with increasing speed because of the ratio of drags from the canopy and jumper.

But then as a separate issue doesn't my argument say that the glide ratio will remain the same at any speed, as the ratio of the drags for the canopy and the jumper will remain the same -- which is counter to Yuri's explanation? On its own, yes.

There's more to that and I'll try to respond when I get the time.

So even if there was an error in the background knowledge for the first part of the Wetswooper's post, the last part of the post still stands as a question to be answered about Yuri's calculation. (That is, the idea of the canopy drag decreasing at low speed just as the jumper's drag does.)

##### Share on other sites
Interesting subject ...
I've start wondering how much the "air speed" increases with the change in WL so I've put together some formulas for which I would love to get your thoughts
Warning - boring content.

In full flight for instance, Lift is perpendicular to the relative wind (it has an angle horizon = AoI + AoA ). Weight is oriented straight down (perpendicular to the horizon) so in other words:
L * cos (AoI + AoA) = W (your total weight)
and since
L = 0.5 * Cl * Density * S * V^2 (lift formula) and
W = m * g = WL * S * g (because WL = m / S)

we get
0.5 * Cl * Density * S * V^2 * cos (AoI + AoA) = WL * S * g

which we can re-write as
WL * g = 0.5 * Cl * Density * V^2 * cos (AoI + AoA)

The last expression implies that the air speed doesn't depend on the Wing Surface Size, it depends only on the WL. Meaning that a 1:1 230 Spectre will fly with the same air speed (not L/D) as 1:1 97 Spectre (assuming that the airfoil, trimming and AoA doesn't change within canopy class - which might not be true).

using the last formula I've computed the new air speed after a downsize from WL1 to WL2 to be V2 = V1 * sqrt (WL2/WL1).
As you downsize from WL 0.6 to WL 1.2 your air speed will increase 1.4 times.

This is true only if we assume that Cl (AoA mainly) and AoI doesn't change as the WL changes which again might not be true because if the L/D changes as you downsize the AoI its changing too.

Does it makes any sense?

Edit: I've used mass as a force and forget to multiply it with the gravitational acceleration. Doesn't affect the last expression since g gets reduced.
Lock, Dock and Two Smoking Barrelrolls!

##### Share on other sites
Quote

Jeez, you almost had me there for a moment!
.....

RIGHT: speed doubles, so the drag increases by 2 to the power 2 = 4
So the drags become 4*4= 16, and 2*4= 8, which is still a 2 to 1 ratio.

Speed therefore doesn't change the inherent balance between the drag of two objects, so no matter where they are acting as a lever on each other, things won't go out of balance as the speed changes.

Yep, thanks. Seems that I was the one that didn't think first..
But still, doesn't it matter drag of the canopy increases by 8 and the drag of the body by 4? The ratio remains the same but the absolute drag forces of the canopy increase more.

##### Share on other sites
Meaning that a 1:1 230 Spectre will fly with the same air speed (not L/D) as 1:1 97 Spectre ***

Don't the shorter lines on the smaller canopy reduce drag and increase airspeed? The smaller canopy will have a reduced airfoil thickness. Your theoretical approach regarding wing size and airspeed might be correct, in practice parasitic drag is a factor (airfoil and lines). Also since the weight is proportionately smaller on the smaller canopy to produce the same wingload it seems reasonable that the smaller weight (a person) would present a smaller surface area, another change in drag.
Sometimes you eat the bear..............

##### Share on other sites
Quote

As you downsize from WL 0.6 to WL 1.2 your air speed will increase 1.4 times.

Yes, speed increases with the square root of the wing loading change. (and the glide ratio stays the same)

That's the basic, ideal calculation, but then, like Martini was talking about, you get into things like canopy distortion, lines and jumpers not changing size, etc. to mess things up.

The basic theory is still a good starting point though.

##### Share on other sites
One could argue that the increase in drag on the bigger wing doesn't change the air speed it only decreases the L/D (since we make more drag for the same lift) .... but I don't think it holds water ... if anything the opposite it's true. A higher wing has a higher L/D.

To bad, it looked so nice on paper....
Lock, Dock and Two Smoking Barrelrolls!

##### Share on other sites
This topic has been exhaustively studied by PhD's.
Instead of trying to re-invent the wheel, just read copies of their reports.
A good place to start is here:

http://www.parapublishing.com/sites/parachute/information/reports.cfm
"There are only three things of value: younger women, faster airplanes, and bigger crocodiles" - Arthur Jones.

##### Share on other sites
Great! That's exactly what I was looking for in another thread.

The thread has led me to some other info/conclusions. I appreciate the help!

Chris
"When once you have tasted flight..."

##### Share on other sites
I'll look into it! Thanks Robert!
Lock, Dock and Two Smoking Barrelrolls!

##### Share on other sites
skydiving canopies are never trimmed for best glide. They are trimmed for best opening characteristics.

measured in best glide a Cobalt tandem is 4.5 l/d.
we use a reinforced version of this canopy on our 2200 pound guided systems for the military and have demonstrated flights of over 20 miles.

Smaller Cobalts glide ratio will vary depending on the size and pilot.

The highest glide ratio canopy we have built to date was for DARPA and is 8.2:1

Highest glide ratio for a non freefall deployable canopy to date is 10.1 (not very stable)
Daniel Preston <><>
atairaerodynamics.com (sport)
atairaerospace.com (military)

##### Share on other sites

This totally makes sense. In the first approximation, speed depends only on wingloading (given the same coefficient of lift and drag). A 230lbs exit weight jumper and a 150lbs exit weight jumper can fly a 230 Spectre and 150 Spectre, respectively, side-by-side touching their endcells without giving any input to equalize the speed.

If we take the drag on the jumper into account, however, a smaller canopy with light jumper should fly a little bit slower and with a little bit worse glide ratio than a heavy jumper on a big canopy with the same WL. To see why, imagine an extreme scenario: a 1lbs carton cutout of a person's silhouette (full size) under a 1sq.ft. Spectre.

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

##### Share on other sites
Thanks yuri, you've made my day!
Lock, Dock and Two Smoking Barrelrolls!

## Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.
Note: Your post will require moderator approval before it will be visible.

Reply to this topic...

×   Pasted as rich text.   Paste as plain text instead

Only 75 emoji are allowed.