Formula for maximum sail speed vs wind speed?

[shawn13]

Can anyone point me to a link that would provide me with a formula for the maximum speed you can travel vs wind speed?

Two Examples:

13m Xbow/Sector 60 V5
Wind Speed: 13kts
GPS Recorded Speed: 22kts

10m SB/138cm Twintip
Wind Speed: 21 kts
GPS Recorded Speed: 26kts

Im trying to calculate the maximum speed I could achieve in those winds. Obviously board/kite are variables, but im wondering if theres a terminal velocity that can be reached like with gravity?

[Hansen Design]

There is no set terminal velocity formula since it is entirely a matter of efficiency.
Here are a couple of benchmarks:
1) 500 meter record held by Paul Larsen with Vestas Sailrocket 2 at 65.45 knots in winds in high 20's knots.
2) Emirates Team New Zealand recorded a top speed for America's Cup 72-foot catamarans at 44.15 knots with a wind speed of 15.8 knots.

[edt]

terminal velocity in gravity is easy to calculate because there is only one source of friction, the air against the object falling so if you know the coefficient of friction, the gravitation constant and the constants of the air you can create a single formula depending on these constants and a power of v.

For kiting there are too many difference sources of friction. There is the water, the calmer the water (and the shallower the water <-- this is why you can't get a record in less than 6 inches of water the less the friction) source of friction from the shape of the board, there are the various sources of friction from the kite, sources of friction from the lines and sources of friction from the rider. So you have at least 3 different parameters dealing with kite, angle of attack the functions of lift and friction, then at least 4 more parameters dealing with the rider, the lines, the water and the board.

So unlike the falling body with just 1 parameter (the coefficient of friction of the falling body) you have 7 different ones for a kite and they interact with each other.

[BWD]

In lighter winds higher multiples of wind speed are usually more achievable, for various reasons.
Ratios tend to be 2-3X TWS for various efficient kiteboard, windsurf and small foiling things.
Depends on many variables though, mostly ones affecting drag, as noted above.
Of course in stronger winds, is when most craft hit their highest speed, more a question of how much you can take/control than how efficient.
Then there is sailrocket, taking things to a higher level.

Usually the easiest way to go faster across or downwind is use a narrower board, at the expense of all-around versatility and low end.
I've hit speeds in the 20s with a 17 and a skinny (35cm) directional in about 10-12 knots.
Kind of a neat feeling - really fast and quiet with a big kite and little bar pressure feeling - but I got downwind fast and had to walk back, no hope of even maintaining a beam reach.

Adding upwind, wide boards, big fins, etc. and it gets more complicated.
But the short answer probably still is going to be between 2-3X windspeed on beam reach or lower.

[JS]

As others wrote, it's a matter of efficiency, specific for each combination of gear and rider.

There's no practical formula for each combination. There's certainly an upper limit for each combination, but experimentation is the only practical way to estimate it.

Also, the relationship between true wind speed and maximum board speed for a particular kite, board and rider (assuming ideal technique, point of sail, sea condition, etc) is not linear.

[Slappysan]

Iceboats can get like 5x times the wind speed.

[plummet]

If your going 1.5 times the wind speed.... that's good.
2 times awesome.
3 times...... insane!

[edt]

the lower the wind speed the easier it is to get a multiple so for instance when the wind is blowing 7 or 8 knots, with a raceboard and racekite in perfect conditions, a 3x or more wind speed is not too difficult. I'm much more impressed with 1.3x wind speed when it's blowing 40 knots.

[zfennell]

of course, the answers have not changed since the first response since they are all correct

but a formula does exist...sort of

peak velocity occurs when thrust=drag

now all you need to do is control those two parameters to your best advantage

[shawn13]

the lower the wind speed the easier it is to get a multiple so for instance when the wind is blowing 7 or 8 knots, with a raceboard and racekite in perfect conditions, a 3x or more wind speed is not too difficult. I'm much more impressed with 1.3x wind speed when it's blowing 40 knots.

Yes I noticed this too. Especially yesterday when it was nuking but I wasnt achieving much more than Mondays run in lighter wind. I figured there was a maximum you could hit after friction and air resistance...

of course, the answers have not changed since the first response since they are all correct

but a formula does exist...sort of

peak velocity occurs when thrust=drag

now all you need to do is control those two parameters to your best advantage

Great this is what Im looking for. Now I just need to calculate the balances. I know i cant calculate and exact because so many factors, but if i can make assumptions on some constants at least I can get a ballpark figure.