Scaling laws and foiling

[tlouth7]

Now that the offshore maxi trimarans are properly foiling, is there still an advantage to them being very big?

Is there a fundamental reason why a large boat with a big rig but also foils that need to generate more lift should be faster in absolute terms?

 

[jehardiman]

Now that the offshore maxi trimarans are properly foiling, is there still an advantage to them being very big?

Is there a fundamental reason why a large boat with a big rig but also foils that need to generate more lift should be faster in absolute terms?

Yes, there is a reason why they are larger...and it has to do with the word "offshore".
Read this 14 year old post about why offshore distance racing vessels get larger to go faster.
Canting Keel Monos vs Multihulls https://www.boatdesign.net/threads/canting-keel-monos-vs-multihulls.13511/page-5#post-104220
Since you joined in 2013, reading the whole 2006 canting keel vs multi thread may lay some ground work. It has some pockets of gold and some pockets of ick, but overall I think it is a fairly balanced discussion of the nuances.

 

[Doug Halsey]

Now that the offshore maxi trimarans are properly foiling, is there still an advantage to them being very big?

Is there a fundamental reason why a large boat with a big rig but also foils that need to generate more lift should be faster in absolute terms?

A few years ago, I ran some VPP comparisons of my foiler Broomstick and a 1/4 scale model, assuming foil & sail areas scaling by length ^2 and weights scaling by length ^3.

Without any constraints on heeling moment and pitching moment, the model was slightly faster, but when those constraints were imposed, the full-scale boat was about twice as fast.

I suspect that the fastest ocean-going foiler will turn out to be one that can keep pushing in more extreme conditions, rather than one with the best theoretical efficiency.

 

[tspeer]

Talking scaling alone, Froude scaling is appropriate for hydrofoils. If weight scales as length^3, foil area scales as length^2, and you want to maintain the same lift coefficient, then the speed needs to scale as sqrt(length). In other words, the two craft need to operate at the same Froude number. This is because hydrodynamic lift varies with speed^2 times area. So sqrt(speed) makes up for the missing dimension in the scaling of area compared to weight.

However, cavitation does not scale. The cavitation-limited top speed of both boats will be the same. If both boats take off at the same Froude number, the smaller boat has a larger range of speed between takeoff and the onset of high-speed cavitation. This is why small boats benefit more from hydrofoils than large ones.

 

[tlouth7]

Yes, there is a reason why they are larger...and it has to do with the word "offshore".

Ah, a very good point that I hadn't thought of. Crew + stores + accomodation weight decreases as a proportion of total as the size of the boat increases.

Talking scaling alone, Froude scaling is appropriate for hydrofoils. If weight scales as length^3, foil area scales as length^2, and you want to maintain the same lift coefficient, then the speed needs to scale as sqrt(length). In other words, the two craft need to operate at the same Froude number. This is because hydrodynamic lift varies with speed^2 times area. So sqrt(speed) makes up for the missing dimension in the scaling of area compared to weight.

So to turn that round, at equal design speed and desired lift coefficient the larger boat would need proportionally larger foils? That sounds like a win for the smaller boat to me!

However, cavitation does not scale. The cavitation-limited top speed of both boats will be the same. If both boats take off at the same Froude number, the smaller boat has a larger range of speed between takeoff and the onset of high-speed cavitation. This is why small boats benefit more from hydrofoils than large ones.

Interesting, I would have guessed that there would be a scale factor to cavitation.

All in all the impression I get is that with foiling size =/= speed in quite the way it does for conventional boats, which is good news for the cost of innovation!

 

[Doug Halsey]

Talking scaling alone, Froude scaling is appropriate for hydrofoils. If weight scales as length^3, foil area scales as length^2, and you want to maintain the same lift coefficient, then the speed needs to scale as sqrt(length). In other words, the two craft need to operate at the same Froude number. This is because hydrodynamic lift varies with speed^2 times area. So sqrt(speed) makes up for the missing dimension in the scaling of area compared to weight.

Are you saying that the top speeds of similarly-shaped foilers should vary as sqrt(length)? Just like heavy displacement boats?

 

[Iridian]

Talking scaling alone, Froude scaling is appropriate for hydrofoils. If weight scales as length^3, foil area scales as length^2, and you want to maintain the same lift coefficient, then the speed needs to scale as sqrt(length). In other words, the two craft need to operate at the same Froude number. This is because hydrodynamic lift varies with speed^2 times area. So sqrt(speed) makes up for the missing dimension in the scaling of area compared to weight.

However, cavitation does not scale. The cavitation-limited top speed of both boats will be the same. If both boats take off at the same Froude number, the smaller boat has a larger range of speed between takeoff and the onset of high-speed cavitation. This is why small boats benefit more from hydrofoils than large ones.

Why would the size of the foil matter for cavitation, assuming a similar cross section?

I believe the reason small boats benefit so much more from hydrofoils than large ones is because of a lower hull speed, and a larger relative resistance from waves..

 

[tspeer]

I misspoke in my description of Froude scaling. What I should have said is with Froude scaling, velocity is scaled with the square root of length. So the hydrodynamic forces that scale as area*velocity^2 now scale as area*sqrt(Length)^2, which is proportional to Length^3.

 

[Doug Halsey]

...I believe the reason small boats benefit so much more from hydrofoils than large ones is because of a lower hull speed, and a larger relative resistance from waves..

If you exclude kites, Moths, and other very small foilers with features that are difficult to scale up, would you still say that smaller boats benefit more?

 

[tspeer]

The lower hull speed of the smaller boat is the same thing as the lower speed from operating at the same Froude number.

Say you built a quarter scale AC75 - a dinghy sized 19 footer instead of a 75 footer. If the AC75 takes off at 18 kt, the dinghy will take off at 9 kt. Both boats will have difficulty getting past 50 kt because of cavitation. So the AC75 will have a speed range of 32 kt, while the dinghy will have a speed range of 41 kt. The AC75 will be able to get to 278% of its takeoff speed, while the dinghy will be able to get to 556% of its takeoff speed. If it takes 12 kt of true wind for the AC75 to take off, the dinghy will require 6 kt of true wind (assuming both boats can reach the same boatspeed/windspeed ratio).

 

[DogCavalry]

I followed the link Jehardiman kindly provided. I must say, Doug Lord is passionate to the point of religious zealotry. And good for him. How else would mountains get moved? He certainly has the energy to do so, the way he moves the goal post around.

 

[CT249]

The lower hull speed of the smaller boat is the same thing as the lower speed from operating at the same Froude number.

Say you built a quarter scale AC75 - a dinghy sized 19 footer instead of a 75 footer. If the AC75 takes off at 18 kt, the dinghy will take off at 9 kt. Both boats will have difficulty getting past 50 kt because of cavitation. So the AC75 will have a speed range of 32 kt, while the dinghy will have a speed range of 41 kt. The AC75 will be able to get to 278% of its takeoff speed, while the dinghy will be able to get to 556% of its takeoff speed. If it takes 12 kt of true wind for the AC75 to take off, the dinghy will require 6 kt of true wind (assuming both boats can reach the same boatspeed/windspeed ratio).

Do we know whether a quarter scale AC75 would reach anywhere near 50 knots, considering that Moths and small foiling cats (ie Nacras, C Class) don't get anywhere near that sort of speed?

I thought that the AC75s flew from about 6.5 knots of wind?

 

[Iridian]

If you exclude kites, Moths, and other very small foilers with features that are difficult to scale up, would you still say that smaller boats benefit more?

Something like a NACRA Inter 20 FCS is capable of 30+ KTs. I think a trimaran could go even faster.

 

[philSweet]

Eighteen knots boat speed, six and a half TWS. That sounds about right for an AC 75

 

[CT249]

I believe the reason small boats benefit so much more from hydrofoils than large ones is because of a lower hull speed, and a larger relative resistance from waves..

Many small boats don't seem to benefit enormously from foils. The World Sailing Small Catamaran Handicap Racing Formula uses what is probably the world's largest small-cat race performance database and it claims that full foilers are only 4% faster than non foilers. Adding foils therefore increases performance less than adding a spinnaker in most cases. It's significant but from many angles it's hardly earth-shaking, and therefore there may be no basis for any claim that small boats benefit more than large ones in general.

Good foilers tend to be of types that don't suffer from significant extra drag at hull speed anyway. A boat that has a significant issue with hull speed is probably not going to be a great foiler in terms of actual all-round performance.