Approximate sailboat speed prediction

Learning to sail in light winds will make you a real sailor. Anyone can do a reasonable job of it in moderate wind strengths, but you really have to focus in light, so the skipper that learns in light air, will have an advantage in all wind strengths.

 

That's good to hear, because there is no choice on weather conditions I can have here - it's either a calm 90% of the time, or a storm

I'm still not getting used to how quickly discussions on Boat Design Forum go sideways. Here I was, hoping to work out a formula to determine speed of a sailboat, and here we are, discussing what makes up a real sailor! Not complaining, just saying Probably my initial discussion about speed prediction was a dead end.

 

Returning, according to your desires, to the origins of the original question, there is no formula to determine the speed. There are various formulas to determine the viscous resistance, wave making resistance, etc. Combining these formulas some scholars have created algorithms to predict the speed depending on the power of the vessel. But they must know many variables of the ship concerned which leads to other formulas to calculate these variables.
So my answer is that there is no formula.

 

I predict that it will reach 2.0 kts in 5.71 kts of apparent wind, 3.08 kts in 8.6 kts of apparent wind, and 3.71 kts in 10.4 kts of apparent wind.

The reason I use the Phrase "apparent wind" is because the boat's speed and route, relative to the wind, will be a significant factor in wind speeds this low.

 

That is very accurate claim, sharpii, but how did you figure it out without me even giving you basic hull shape data, as well as info on rig, weight distribution and so forth? Or am I missing a joke?

 

If I told you, I'd have to kill you.

Nah. Just kidding.

My predictions are based on the following assumptions:

1.) It takes 5.0 lbs of thrust, per 100lbs of boat, to push that boat to what I call Waterline Length Speed. That is (WL Length)^0.5. For your boat, that is about 3.08 kts.

2.) The wind pressure on sails is: ((wind speed in kts)/16.2)^2

3.) The sail on your boat will be about 80% efficient

4.) Because your boat is supposed to have a Prismatic coefficient (cP) in the low 0.50's, it will reach lower speed thresh holds sooner, at the price of reaching higher ones later. WL Length speed is a lower thresh hold.

5.) the thrust needed for a higher speed is: (higher speed/lower speed)^2 (if I'm wrong about this, someone please correct me)

So now that I have made these assumptions, let's plug in the numbers.

Your boat will displace about 400 lbs, with you and your girlfriend on it.

Your boat will have about 80 sf of sail.

First we'll use the 5 lb per 100 lb assumption, then we will multiply that by 0.9, to account for the lower cP.

So: 400 lbs/100lbs*5 lbs*0.9 = 18 lbs thrust.

18 lbs thrust/(80 sf*0.8)= 0.28 lbs thrust/sf of sail.

Now we need to do a bit of algebraic shuffling.

Thrust = ((wind speed in kts)/16.2)^2

becomes

(thrust^0.5)*16.2= required wind speed

So

(0.28 lbs thrust ^0.5)= 8.57 kts wind speed to attain WL Length speed.

The other wind speeds for the other boat speed thresh holds were easier to calculate due to assumptions 2.) and 5.), where the square of the increased wind is canceled out by the square of the increased boat speed.

So, I got my wind speed, in kts, for my boat speed at 2.0 kts by simply dividing the new speed by the faster old speed, and multiplying the old wind speed by this product.

Hence:

(2 kts boat speed/3 kts boat speed)*8.57 kts wind speed = 5.71 kts wind speed.

So my predictions are just as precise as the accuracy of my assumptions. No more, no less.

Time and experience will tell.

 

I second Pars motion that learning to sail well in light air makes a better than average sailor......unless you die of frustration first. Or maybe you wear your neck out because you were constantly watching the mast head fly.

Sharpii2 you are using the number 16.2 in the denominator of some of the calcs. Is that slug/2 ? My tired old brain is trying to recall the physics involved in the calculations.

 

I see.

I made an error in presenting my equation.

(0.28 kts thrust^0.5) = 8.57 kts wind speed.

should be

(0.28 lbs thrust(per sf of sail)^0.5) * 16.2kts wind speed/pound thrust = 8.57 kts wind speed.

Sorry. My bad.