Math Nerds - Help! - Calculate Swept Path

I believe the answer to this question is much simpler than I’m trying to make it, but I can’t figure it out.

What is the formula for calculating the width of a ship track with each additional angle of crab?

600’ x 106’ ship. With zero crab angle, track through water is 106’ wide.

When holding up for 3 degrees of set, what is the width of the track through water? 140’, 160’?

Somebody told me once that at 5 degrees you double the width of the ship (in this example, 212’), but I can’t figure out if this is accurate or not.

Any of the smarter ones around here have an idea on how to calculate this???

I don’t know the definition of track width, but it sounds like a right triangle problem where the ship length is the hypotenuse and the crab angle is theta.

why not say Cos of crab angle is track width over length?


It’s called sweep path.

The additional width = LOA * Sin (drift angle)


So for a 600’ at 5 degrees, it’s an additional 52 feet? So your sweep path (thank you for that proper terminology) is 158?

Oh ya, Sin. I had the wrong angle mind for crab.

I don’t think that there is a formula for this unless it is loosely related to the formula for squat.
Which is bollocks.
What are the wind conditions?
What is the swell?
What are the local top and bottom layer currents?
Subsea contours?
What is your hull form?
Trimmed by the head or by the stern?
Where is my gin?
Sorry, last one was just a plea for help:)

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While I sort of agree with you, I’m looking for some numbers to make an argument one way or another for certain reasons. Knowing how wide the ship becomes when crabbing is helpful for this.

Yeah, I get 52 feet, plus your beam.

If you have to calculate sweep path you’re not going to have a good day.


Yea, well, that’s why I’m trying to calculate it. To avoid that.


There is no formula that you can rely on!
It is futile.
If you are part of a management team attempting to lay down fixed rules for Bridge Teams to apply then good luck with that.
If it is a an academic exercise then go out and try it!

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Instead of a right triangle, I used a wrong triangle: dumb snipe.


“Rate * time = distance” has never let me down.

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Also 60 * D = S * T

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There’s always LSMFT. Worked for my grand uncle.

For crying out loud, none of those will work in real time conditions, ergo they are useless.
What is the formula for the Master to assess the effect of the wind on the ship whilst coming alongside?

Force in tons = (area/1000) (velocity squared / 18 )

Area in meters. Velocity is in meters per second (approx half of the value in knots)


The formula for the swept path is SP = B + LOA * sin α

It should be noted that the term LOA * sin α is a simplified expression but for practical use It is sufficiently accurate.


Wouldn’t it really be somewhat less? I think this formula assumes the pivot point is at the bow.

There is no pivot point, just a bit of trig showing the shadow cast by the bow on your wake, so to speak. You can work it out as two triangles with the tips midship, but the answer is exactly the same.