Formula to calculate if sail change is really worth it
Post by iconPost by UR2L8 | 2017-12-20 | 01:30:59

Lets say I gain 0.1 knots, going from 25 knots with HG to 25.1 with C0.
It takes 75 seconds with no speed for sail change... (or is it 75 seconds with reduced speed, like half the speed?).

Anyway, how many hours do I need to go with C0 with this gain of 0.1 for it to be worth while? Let's assume constant TWA and constant windspeed.

So I made the following formula

NS = New speed after sail change
CS = Current speed (before sail change)
75/3600 = 0,020833h = penalty in hours for sail change.
T = time (hours)

Formula is derived from NS x (T-0,020833) = CS x T
which give
T = NS x 0.020833/(NS-CS)

So in the above example
25.1 X 0,020833/0.1 = 5.229 hours = 5h 15 min


commenticon 16 Comments
Post by iconPost by Ursus Maritimus | 2017-12-20 | 08:53:19
calculate with same distance: 25 knots at 50% during 75 s gives you (0,833 - 0,582) = 0,251 nm distance loss between updates (120 s)

so you need 0,251 / 0,1 = 63,1 updates, so 63,1 x min = 126 min = 2h 6 min

this is half your value. looking at the formula, the time loss is HALF of 75 s, because you sailing at HALF speed not at a complete stop. than the numbers match
Post by iconPost by Ursus Maritimus | 2017-12-20 | 08:57:54
interesting to see the last bit: everyone on C0 and drag the last bit to the line or change to LG with a penalty ?
Post by iconPost by UR2L8 | 2017-12-20 | 11:50:35
Thank you DancingDjMike for the correction!
Post by iconPost by UR2L8 | 2017-12-20 | 12:00:26
But I actually arrive to a different result. I will double check, probably just did a mistake

So the penalty is 75 seconds with half the speed of the current speed if I understood correctly?

Post by iconPost by GeGaX | 2017-12-20 | 14:09:46

Post by iconPost by GeGaX | 2017-12-20 | 14:13:31
speed = 50% for, 75 sec if you have Winchs Pro, 300 sec if you have not
Post by iconPost by UR2L8 | 2017-12-20 | 15:36:55
Yes and the penalty is half of the speed with the current sail? Or with the new sail? I suppose its the current sail.
Post by iconPost by WaterHammer | 2017-12-20 | 16:13:52
I suppose with the new sail
Post by iconPost by zezo | 2017-12-20 | 16:15:02
They are supposed to be close at the crossover point, but should be with new sail and new wind.
Post by iconPost by Ursus Maritimus | 2017-12-20 | 22:41:29
penalty is AFTER the sail change, so with the new sail.

you regain the penalty loss by the higher speed with the new sail and can calculate the ROI

rule of thumb:
- in distance, you loose 1% of you current boat speed (nm per hour)
- divide that distance by the gain in speed (nm per hour) and you have the break even time (in hours)
Post by iconPost by zezo | 2017-12-20 | 16:17:33
As a rule of thumb 75 seconds at half speed is close to 36 seconds standing still, which happens to be 1/100 of hour.

That means you lose about 1% of your speed, so at 25 knots loss is 0.25 miles. 4 times more without winches.
Post by iconPost by DeepBrine | 2017-12-20 | 16:23:27
Now if only I could get the first 300 boats to do 25 sail changes in the next 20 hours...

Post by iconPost by UR2L8 | 2017-12-20 | 20:43:08
Ok, if its with the new speed, then I suppose the formula above becomes

NS x (T-0.020833) + NS x (0.020833/2) = CS x T
-> T =NS (0.010416) /(NS-CS) Which then gives 2 hours and 37 minutes

I think DancingDjMike made some small calculation error somewhere and would have arrived at the same result

With the same calculation as DancingDjMike I get
Distance loss during two minute intervall is
25.1 x 2/60 - (75x25.1/2 + 25.1x45)/3600 = 0.261458333 nm distance
--> 0.261458333/0.1 = 2,6145 hours = 2 hours and 37 minutes. So different way to calucate, but same result. Formula verified :-)
And in terms of updates (every two minutes) its 78.4 updates
Post by iconPost by Ultimate Victory | 2018-01-02 | 15:34:02
Does the penalty is applied twice if you gybe/tack and change the sail at the same time ?
Post by iconPost by zezo | 2018-01-02 | 18:04:30
Yep. Speed is 1/4. Which is slightly better than double time with half speed.
Post by iconPost by Ursus Maritimus | 2018-01-02 | 21:12:31
yep, the second penalty only counts half, because it is 50% of the already reduced 50% speed.
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