Power Kite Forum - Airspeed -vs- Force

Airspeed -vs- Force

PistolPete - 24-5-2013 at 03:40 PM

Did some simple calculations to see what’s needed to get pulled.

Upload picture sizes are small, need to click on pictures to enlarge...

PistolPete - 24-5-2013 at 03:42 PM

The two attached graphs (sheeted-in & sheeted-out) illustrating the pulling force of a kite in varying airspeeds. This is based on simple calculations using the lift coefficient equation and is intended to show a few conceptual relationships only. Estimations/ Inaccuracies include:
- Kite is not an ideal foil-bearing body
- Kite planform area is not uniform
- Kite chord varies and is flexible
- Inefficiencies unaccounted for
- Lift Coefficient values vary
- Air Density values vary
- And many more…

The illustrations have a color overlay indicating a notional limited usable range. There are calculated curves for 5, 10, and 15 square meter planform/projected area kites. This is different than the typical windrange-vs-kite size correlations. Hopefully this helps to visualize the magnitude of force at various airspeeds, using different size kites. What is not included is the direction of the force (vector), which helps determine how useable the force will be.

Airspeed is calculated as a function of force in the illustrations. Beach windspeed (true wind velocity) is easy to visualize with a steady kite as it is equal to the kite airspeed (apparent wind velocity). As soon as the kite moves, the apparent wind velocity changes. The kite can be moved by steering (sine-ing) and/or being set in motion from sailing. Y-axis airspeed can be visualized using three different perspectives:
(1) As beach/true wind velocity (for forces seen static flying)
(2) As kite/apparent wind velocity (for total forces seen at the kite)
(3) As sailing and/or sin-ing wind velocities (for forces the rider controls)

One of the graphs illustrates the minimum calculated forces for a kite sheeted-out (using CL=0.75) and the other graph illustrates the maximum calculated forces for a kite sheeted-in (using CL=1.7). The two graphs show different usable kite windranges depending on the sheeting of the kite. Again the specific graph numbers may not be accurate to actual kite performance but, this does provide a general idea of the range a depower kite could provide. Many other pro/con variables influence actual airspeed-vs-force curves. Kite shape, rigidity, weight, line lengths, etc… are ignored for mathematical simplicity. The above concepts are all well known, but sometime drawing a picture helps.

Ref:
http://en.wikipedia.org/wiki/Lift_coefficient
http://en.wikipedia.org/wiki/Air_density
http://en.wikipedia.org/wiki/Planform
http://en.wikipedia.org/wiki/Wind_triangle

area429 - 24-5-2013 at 07:39 PM

That's an excellent visual representation! :thumbup:

That is really useful for understanding the wind ranges of my different kites under different conditions. It also drives home how the power of the kite in a lot of ways is tied to the projected area, and not the flat area. Its a wonder companies haven't adopted PA as the industry standard when describing their kites. :D:smug:

It also shows how a kite that goes fast through the window will gain a lot of power! We can all attest to that here! Been on my butt more than once watching the kite rip through the power zone :lol:

Here's a question for ya: Is the air density sufficiently lighter in say the great lakes to noticeably change a given kites wind range in the same conditions? Would you notice in the mountains?

PistolPete - 30-5-2013 at 08:45 PM

Temperature
Attached (click on it to see full size) is a temperature plot for the 10m planform area wing. The blue (lower=less wind needed for pull) lines are for air density for very cold dry air (23°F or -5°C = 1.13Kg/m³ @ Sea Level) and the red (upper=more wind needed for pull) line represents very hot dry air (105°F or 40.5°C = 1.32Kg/m³ @ Sea Level). The biggest difference is on the Sheeted-Out plot because lift efficiency is low so, more wind is needed to make up the difference in air density. Some numbers are:
50lbs of pull sheeted-out needs 1.7mph more wind for hot air (sheeted-in needs 0.8mph).
100lbs of pull sheeted-out needs 2.4mph more wind for hot air (sheeted-in needs 1.1mph).
150lbs of pull sheeted-out needs 2.9mph more wind for hot air (sheeted-in needs 1.4mph).
200lbs of pull sheeted-out needs 3.4mph more wind for hot air (sheeted-in needs 1.6mph).
250lbs of pull sheeted-out needs 3.8mph more wind for hot air (sheeted-in needs 1.8mph).

PistolPete - 30-5-2013 at 08:46 PM

Altitude
Attached (click on it to see full size) is an altitude plot for the 10m planform area wing. The green (lower) lines are for air density for sea level dry air (1.2Kg/m³ @68°F/20°C) and the purple (upper) line represents dry mountain air at 10,000ft/3048m (0.826Kg/m³ @ 68°F/20°C). To show only the altitude differences, the temperatures are held same but, note that would be a warm day that far up a mountain. Some numbers are:
50lbs of pull sheeted-out needs 2.6mph more wind for mountain air (sheeted-in needs 2.1mph).
100lbs of pull sheeted-out needs 3.7mph more wind for mountain air (sheeted-in needs 3.0mph).
150lbs of pull sheeted-out needs 4.5mph more wind for mountain air (sheeted-in needs 3.7mph).
200lbs of pull sheeted-out needs 5.2mph more wind for mountain air (sheeted-in needs 4.2mph).
250lbs of pull sheeted-out needs 5.9mph more wind for mountain air (sheeted-in needs 4.8mph).

PistolPete - 30-5-2013 at 08:47 PM

Humidity
No plots needed for this one. Even for worst case (high temperature) Air Density only varies 0.3% between the full range of 0% and 100% humidity. Dryer air is denser (better for lift) than humid air, because water has less molecular mass than air. If it is raining, your kite will get heavier, and you will lose pull, otherwise humidity is really a non-factor.

PistolPete - 30-5-2013 at 08:48 PM

Wind Gusts
Attached (click on it to see full size) is a plot for gusts-vs-pull assuming 68°F/20°C dry sea level air at 60lbs of steady lift (17mph wind sheeted-out or 11.5mph sheeted-in). For simplicity it is assumed the wind gusts are in the same direction as the apparent wind seen by the kite (worst case). Actual gusts are generally in the true wind direction. The brown (upper) line represents when sheeted-out what gust speeds cause what additional pull. The pink (lower) line represents when sheeted-in what gust speeds cause what additional pull. This plot shows why it can be much more challenging to kite in gusty conditions. And, the lulls that accompany gusts add even more to the challenge (by reducing pull). This plot also illustrates that the effects of gusts/lulls are quite a bit more pronounced when sheeted-in. Some numbers are:
Sheeted-In
4mph gusts while sheeted-in sailing in 17mph winds adds 50lbs of pull
7mph gusts while sheeted-in sailing in 17mph winds adds 100lbs of pull
10mph gusts while sheeted-in sailing in 17mph winds adds 150lbs of pull
12mph gusts while sheeted-in sailing in 17mph winds adds 200lbs of pull
Sheeted-Out
6mph gusts while sheeted-in sailing in 17mph winds adds 50lbs of pull
11mph gusts while sheeted-in sailing in 17mph winds adds 100lbs of pull
15mph gusts while sheeted-in sailing in 17mph winds adds 150lbs of pull
19mph gusts while sheeted-in sailing in 17mph winds adds 200lbs of pull

PistolPete - 30-5-2013 at 08:52 PM

Hi Area 429 - Hope the posts above answered your questions

krumly - 31-5-2013 at 11:33 AM

Nice graphs Pete.

One thing to note is 'efficiency' is a relative term. Under your post on air density at altitude, you mention kite sheeted in as more efficient. It is true that a higher angle of attack results in more lift, up until the kite stalls anyway. But increased angle of attack also results in more drag, and that drag increases at a rate much higher than lift increases. There is an optimum sheeting angle that allows for maximum lift to drag, and that is usually in the range of 5-8 degrees to relative wind, depending on foil section and aspect ratio of the kite. The kite can be flown fast at that angle, and you can point upwind higher. Total lift will be maximized.

Planes fly fast fly at low angles of attack. They only fly at high angle of attack when they need to climb or descend slowly.

krumly

PistolPete - 31-5-2013 at 11:56 AM

Thanks krumly - You are correct :thumbup:

I had a little time to spend so I thought about playing with the variables to see what could happen. Might help understand how conditions may affect a session. Of course most of what affects what in real life becomes more intuitive with more flying/experience ... at least that what us older folks say :P

Scudley - 6-6-2013 at 08:13 AM

Quote: Originally posted by area429

. Its a wonder companies haven't adopted PA as the industry standard when describing their kites. :D:smug:

Projected area on its own is not a great indicator of kite performance. The are so many other aspects that affect kite performance that PA alone is just a number. The difference between two kites of the same PA but with A/Rs of 5 and 3 would seem to make PA totally meaningless as a guage of kite performance. Even line lengths make a difference.
Take my 3m Samurai and 3m Reflex, pretty much the same PA, but very different kites. I would confidently put up the Samurai in winds that had me scared shwitless with the Reflex.
S

Sumanitu - 9-6-2013 at 08:03 PM

Thanks for the awesome explanation of the physics! What is the lift coefficient of your average 3m 2 line trainer kite?

I have a slingshot b3 http://www.amazon.com/Slingshot-B3-Series-Trainer-Kite/dp/B0... which as far as I can tell, has no specs online for it...

Sumanitu - 9-6-2013 at 09:59 PM

Quote: Originally posted by krumly

Nice graphs Pete.

One thing to note is 'efficiency' is a relative term. Under your post on air density at altitude, you mention kite sheeted in as more efficient. It is true that a higher angle of attack results in more lift, up until the kite stalls anyway. But increased angle of attack also results in more drag, and that drag increases at a rate much higher than lift increases. There is an optimum sheeting angle that allows for maximum lift to drag, and that is usually in the range of 5-8 degrees to relative wind, depending on foil section and aspect ratio of the kite. The kite can be flown fast at that angle, and you can point upwind higher. Total lift will be maximized.

Planes fly fast fly at low angles of attack. They only fly at high angle of attack when they need to climb or descend slowly.

krumly

This is true, but the graph lines of force would still be accurate. Increased angle of attack means increased drag, lower speed of the kite through the window, increased lift coefficient, and a net lower force.

PistolPete - 24-10-2013 at 10:29 PM

Hey - Another opportunity to calculate force :P

area429 - 25-10-2013 at 05:22 PM

Lol

My head's spinning..

skimtwashington - 25-10-2013 at 06:33 PM

This thread is related to this recent thread:
http://www.powerkiteforum.com/viewthread.php?tid=26885#pid259687

Temperature, humidity, altitude...Not all same speed wind is same force..I'm getting from this.

AoA, shape, aspect ratio,......nor all same meter size kites have same pull, upwind ability, stability, ....

Need more than just a simple wind meter....need a base camp computer station to calculate all the variables and pick a kite from quiver! :lol:

BTW....Guy in kite looping fail was hurt if I recall...

crabnebula - 26-10-2013 at 05:46 PM

I love physics I really do