Performance Number

[migliore 0]

So we all know that wing loading is a good number to use to get a feel for how a canopy will behave for a jumper of a given exit weight. But, a canopy's performance is also governed other factors such as line length. For example, lines are generally shorter on smaller canopies and thus make smaller canopies respond quicker to control inputs (see [URL] http://www.performancedesigns.com/docs/wingload.pdf [/URL]).

So I got to thinking about a new (I think) measure of canopy performance that I call a Performance Number. Basically, this number starts with your normal wing loading and increases it as the canopy size becomes smaller than 200 sq.ft. and as the canopy becomes more elliptical.

The variables used are:
PN = Performance Number
W = exit weight of jumper
A = area of canopy (size in sq. ft.)
L = scaling variable to compensate for line length
S = shape (cut) of canopy

For this example, I define L = 0.5.

S can be one of 3 values: 0 for fully-rectangular canopies, 0.25 for semi-elliptical canopies, or 0.5 for highly-elliptical canopies.

The actual equation is:

PN = (W/A)*((200/A-1.0)*L + 1.0) + S


EXAMPLE 1:
Jumper weighing 238 out the door flying a Sabre I 170.
W = 238 lbs.
A = 170 sq.ft
S = 0.0 (square)
The resulting wing loading is 1.40 and the Performance Number is 1.52

EXAMPLE 2:
Jumper weighing 168 out the door flying a Stiletto 120.
W = 168 lbs.
A = 120 sq.ft
S = 0.5 (elliptical)
So, while this jumper's wing loading is also 1.40, their Performance Number is 2.36


Please play around with this method and let me know your thoughts. I would like to get some feedback from some of the more experienced jumpers who have flown large ranges of canopy sizes and shapes. Obviously, this formula doesn't include compensation for crossbraces or airlocks, but this could easily be added. Also, the value of L can be changed to make the effect of flying a small canopy larger or smaller.

Shane

[billvon 2,396]

I think that would be very hard to do. It's like trying to come up with one number for the performance of a vehicle, and then claiming that a Harley-Davidson performs better than a Hummer.

There are so many things that makes a canopy better or worse. Where is recovery arc length in that equation? A Stiletto might equal the same size Katana on that formula, but their arcs are _totally_ different. That makes a Katana a better (and even safer) choice for a swooper, but a worse choice for a newer jumper. Where's trim angle? Steeper generally gives you better planeouts but reduces glide. How about stability in turbulence? For those of us who spend time in places like Perris that's a pretty important part of canopy safety.

And what would the purpose of this be, anyway? Would it be used to judge what someone is ready for? In that case, "danger factor" would probably be a better term; better performing canopies are often safer. If it _is_ a danger factor, you have to add in opening performance, sensitivity to body position during opening and stability in brakes after opening. (A canopy that can mal because one shoulder is low isn't a very safe canopy for a new jumper to be jumping.)

[MikeTJumps 4]

Ah, the Physicist in you is getting ready to write a paper for inclusion in a journal.

That is a neat idea (your formula).

Mike Turoff
Instructor Examiner, USPA
Co-author of Parachuting, The Skydiver's Handbook

[sducoach 0]

Bill,

Agreed. Also, performance is also determined by your frame of reference not just the capabilities of the canopy. The base line that needs to be established for this type of "rating" to work is constantly shifting due to the experience level and perception of the canopy pilot.

Good thoughts however very difficult to utilize.

Blues,

J.E.

James 4:8

[mr2mk1g 10]

As an exercise in physics or out of interest it's a cool idea. Not sure if it has an application to safty or in judging what people are ready to jump.

I think you're off to a good start, but as highlighted above, the equation needs to be much much longer. There are just so many variables in this sport.

[migliore 0]

I did not intend for this method to be applied to today's extreme canopies. As Bill said, there are just too many variables to compensate for with these canopies. As such, Velocities, Katanas, VX's, etc. should not come to mind when considering this method.

I think the target audience is younger to intermediate jumpers who would like to get a feel for how a different canopy size or shape would perform. The idea being that smaller jumpers can see that their WL does not need to be as high as a larger jumper to get similar performance and that canopy shape plays a significant role in performance. Of course, all changes in size and shape should always be made gradually and with the consent of a JM or S&TA.

Also, I can understand if the name isn't quite right. It was just the best I could come up with at the time. However, I think Danger Number is a bit too extreme.

Shane

[billvon 2,396]

>The idea being that smaller jumpers can see that their WL does not
> need to be as high as a larger jumper to get similar performance
> and that canopy shape plays a significant role in performance.

So the idea is to let newer jumpers choose higher performance parachutes that are larger? The Silhouette and the Pilot are two parachutes designed for that purpose, but both wouldn't score very highly on your chart.

[AndyMan 7]

The first weakness I see is " S = shape (cut) of canopy: 0 for fully-rectangular canopies, 0.25 for semi-elliptical canopies, or 0.5 for highly-elliptical canopies.

Keep in mind that the PD Navigator, a student canopy, is "semi-elliptical". So is the PD Spectre.

I would not assume that a Navigator is anymore "high performance", than a Saber 1, which is fully rectangular.

_Am

__

You put the fun in "funnel" - craichead.

[mr2mk1g 10]

In that same vein the Safire II is fully-elliptical but only lightly so, thus generally placed in the semi-elliiptical class.

[AggieDave 6]

Quote

Keep in mind that the PD Navigator, a student canopy, is "semi-elliptical".

Sorry, but no they're not. The other hybrid from PD that's very similar to the Navigator is, though, the Silhoette (sp?).

Navigators are big rectangles, great student canopies actually.

--"When I die, may I be surrounded by scattered chrome and burning gasoline."

[migliore 0]

Quote

So the idea is to let newer jumpers choose higher performance parachutes that are larger? The Silhouette and the Pilot are two parachutes designed for that purpose, but both wouldn't score very highly on your chart.

Thanks for your honest criticisms...that is what I am looking for by posting. But the idea for this method is actually to increase safety by having newer jumpers realize that WL is only one part of the story. Just because Bob has 50 jumps and has a 1.2 WL, that doesn't mean Jen with her 150 jumps (and 100 less lbs.) should necessarily have a 1.2 WL also. It just introduces absolute canopy size into the equation rather than rely solely on the relative size of the canopy vs. the jumper's weight.

I included canopy shape as an afterthought. Some good points have been made that indicate that it may not be appropriate to include shape info.

**One more thing I forgot to mention, this method is NOT for use on canopies smaller than 200 sq.ft. The Performance Number should NEVER be lower than the wing loading.

Shane

[bodypilot1 0]

Quote

and then claiming that a Harley-Davidson performs better than a Hummer.

No, but owning a Harley may get you a hummer?

Sorry, I couldn't pass it up.....

-

www.WestCoastWingsuits.com
www.PrecisionSkydiving.com

[quade 3]

I think the biggest problem is you haven't defined what you mean by the word "performance".

quade -
The World's Most Boring Skydiver

[nightjumps 1]

Any thoughts on the skydiver's size and effect on parasitic drag?

edit: oops, you mentioned over 200 sq.ft.

[Push 0]

I think a better measure of this would take into account actual performance and not structural characteristics. Since we don't really have a coherent mathematical model for a non-rigid wing like a parachute, this would make sense. The performance number should take into account things like turn rate, altitude lost in turns, full flight speed, stall speed, stall point, position of sweet spot, responsiveness to front/rear/weight shift control input (this includes the "spinetto" opening characteristic), glide angle, near-stall descent rate, opening time/speed and consistency of deployment (maybe the standard deviation would work here), length of recovery arc for various inputs (fronts, rears, toggles), etc. Since noone really ever measures these things, assigning performance numbers to various canopies is going to be a very big project.

-- Toggle Whippin' Yahoo
Skydiving is easy. All you have to do is relax while plummetting at 120 mph from 10,000' with nothing but some nylon and webbing to save you.

[FrogNog 1]

Consistency of deployment has at least two deviations, not just one: the first one is how consistently a canopy's openings are. The second one is how consistently other canopies of that same make, model, revision, and assembler are in having the same consistency.

For example, a Model X 150 canopy Joe owns may always open soft. But another Model X 150 canopy Bob owns may always open hard. Each canopy is consistent itself but not with each other.

A Model Y 150 canopy Fred owns may sometimes open soft and sometimes open hard. The other Model Y 150 canopies Al, Charles, and Freako own are exactly the same - with their eyes closed and 100 jumps on any random one of these canopies none of them can tell whether it's theirs or one of the other Model Y 150s. The canopy is not consistent with itself, but it is consistent with each other.

Unfortunately, I don't think this is measurable. It's hard to tell whether a canopy opens well. Some people somehow pack and have body position that works really well for some canopies, vs. others. Line trim would always be an issue, too. I don't think that can be controlled for by just using new linesets, either, because I recall at least one manufacturer saying they mistrim them just a hair at the factory so some of the lines will actually shrink the canopy into trim for a great part of the lineset life.

Just my little addition to the response that "this is a hard question." I think for best chance of success, the formula has to answer as small a question as possible.

-=-=-=-=-
Pull.

[Jimbo 0]

Quote

Quote

Keep in mind that the PD Navigator, a student canopy, is "semi-elliptical".

Sorry, but no they're not. The other hybrid from PD that's very similar to the Navigator is, though, the Silhoette (sp?).

Sorry, but yes they are.

From PD's own web page

Canopy model: Navigator 200
Area (SQ Ft): 200
MIN (Lbs): VLC
STUDNT (Lbs): 130
NOVICE (Lbs): 140
INT (Lbs): 200
ADV (Lbs): 240
EXP (Lbs): 240
MAX (Lbs): 240
SPAN (FT.): 19.07
CHORD (center/end FT.): 9.17/8.05
ASPECT RATIO: 2.52:1

It's tapered, Dave.

Quote

Navigators are big rectangles, great student canopies actually.

Great student canopies, yes. Rectangles, no.

-
Jim

"Like" - The modern day comma
Good bye, my friends. You are missed.

[AggieDave 6]

Hmmmm...I've got probably 40 jumps on Navigators, and I've never noticed it before, it looks just like a big rectangle.

Now, can you really call something wil such a small amount of taper truely a "semi-elliptical" in the same class with canopies like a Diablo or a Sabre2? Although you showed me I was incorrect and that it does have a very slight taper, I just have a hard time putting it into the "semi-elliptical" class of canopies.

--"When I die, may I be surrounded by scattered chrome and burning gasoline."

[billvon 2,396]

> it looks just like a big rectangle.

So does the Silhouette. But it's elliptical too.

>I just have a hard time putting it into the "semi-elliptical" class of canopies.

Semi semi elliptical? Elliptical lite? "I can't believe it's not a square" elliptical?

[Jimbo 0]

Quote

Now, can you really call something wil such a small amount of taper truely a "semi-elliptical" in the same class with canopies like a Diablo or a Sabre2?

It's not square (or rectangular), so I'm not sure what else you would call it. It just goes to support Bill's earlier statement that there's more to the performance (or danger factor) of a canopy than just the cut of the wing.

-
Jim

"Like" - The modern day comma
Good bye, my friends. You are missed.

[Remster 24]

Quote

"I can't believe it's not a square" elliptical?

ROTFLMAO... Is is less filling too?

Dont knwo if you noticed, but on PD's site, they arent using that marketing lingo of fully, semi, tapered, bla bla bla anymore.

Remster

[AndyMan 7]

Thanks Jimbo, I was sure of that - but I didn't know PD published the numers.

Dave - the difference isn't small, either. More than full foot difference between the end and center cells. You should be able to see that.

Comparison to a Saber 2 190 which has a chord of 8.19/7.53, a difference of roughly a about half a foot - you can not calim that the Saber 2 is semi-eliptical but the Navigator is not.

This just reinforces my point that the shape of a canopy is a very poor indicator of its performance.

Popular PD canopies and the differences in chord between center and end-cells:

Navigator 200: 1.14 feet
Specter 190: 0.85 feet
Saber2 190: .66 feet
Stileto 190: 2.72 feet

Clearly these numbers aren't the end of the story because there's a lot more to the "degree of elipticalness" than the difference in chord, also the span and its impact on the aspect ratio is key - but it does give a good indication.

Somebody who knows geometry better than I do can do the math... Please?

_Am

__

You put the fun in "funnel" - craichead.

[Chrisky 0]

I really like that Performance Number idea, as it attributes more factors than just the WL. I'd rather call it a "gear factor" or "risk factor" (gear s my fav)...
I would also consider it more jumper than canopy-related. Like "My gear factor is 2.3 on my 120"... Like the Wingloading, it doesn't say anything about the canopy, but the number would significantly increase if i went to a fully eliptical at same size/WL, thus giving a warning...

Quote

Semi semi elliptical? Elliptical lite? "I can't believe it's not a square" elliptical?

Well, the example was played out in number factors, so how about not being hardheaded and make a "Semi semi elliptical" a 0.05, a slightly more tapered a 0.1 and a strongly tapered a 0.4?

edited for sticky fingers...

The mind is like a parachute - it only works once it's open.
From the edge you just see more.
... Not every Swooper hooks & not every Hooker swoops ...

[billvon 2,396]

>I'd rather call it a "gear factor" or "risk factor" (gear s my fav)...

Ah, now that's very different! A "risk factor" seems like it would describe how unforgiving a canopy is. An old PD150 would have a high risk factor and a low performance factor.

>. . . make a "Semi semi elliptical" a 0.05, a slightly more tapered a
> 0.1 and a strongly tapered a 0.4?

Where do those numbers come from? What't slightly tapered? Is a Diablo less tapered than a Silhouette? I would think you'd have to base that on aspect ratio rather than subjective numbers.

[quade 3]

Quote

I would also consider it more jumper than canopy-related. Like "My gear factor is 2.3 on my 120"... Like the Wingloading, it doesn't say anything about the canopy, but the number would significantly increase if i went to a fully eliptical at same size/WL, thus giving a warning...

Naww, then it just becomes another "bragging rights" number.

If you really want to take the individual jumper into the equation, then add in some sort of currency and overall experience level numbers and call it "Life-flight Probability Factor."

The reality of this that I see is the formula is -way- too complex for most jumpers anyway. Do a quick search on how many times folks have just asked how to figure out simple wingloading.

quade -
The World's Most Boring Skydiver