Wave making resistance

Hello all.

Quite a while ago Mike ?, who has since passed away, posted this equation for wave making resistance taken from D. W. Taylor's book " the Speed and Power of Ships".

Resistance in lb = 12.5*Cb*V^4/L^2*Displ in long tons

I have a couple of queries about it.

1) is the last term, Displ in long tons, intended to be in the numerator or the denominator.
2) I don't feel the equation is dimensionally correct, ie inserting the units on the right hand side will not give the right hand side unit of lbs.

Taylor's book was published in the early 40's, I think, and does not appear to be available now in the bookshops or on library shelves. Consequently, validation of the equation through those means is remote. Does anyone have a copy of the text to verify it or is anyone able to shed some light on it.

Thanks for all help.

 

Curiosity got the better of me this morning, so I pulled out Taylor and tried to find the referenced formula - and I could not. This must be something that Mike derived from the Taylor data. First, when Taylor uses "wavemaking" resistance, he was actually referring to the residuary resistance (Rr).

To answer your questions, Displ is in the numerator. Taylor followed the convention of the time to describe drag figures as resistance in pounds per displacement in long tons. It was not uncommon to use quasi-dimensional ratios, such as drag in pounds per long ton. Consider displacement-length ratio (replaced by CVOL = L / vol^(1/3)) and speed-length ratio (replaced by Froude number).

I followed the trail to see if the formula was a reasonable estimate for Rr/Displ by checking it again two very different models - the USS Yorktown from Taylor (Fig 62) and the UBC trawler model 3. I found that the formula is not too bad for Fn < 0.3 (SLR < 1.0). In this range it did not pick up the humps and hollows, but it did fit the middle of the Rr drag curve. However, above this Fn point it seriously under-predicted Rr/Displ. At Fn = 0.4 (SLR = 1.3), the formula showed only about 50% of the actual drag, with points only 30% of the actual Rr at some speeds above this.

So, this might be useful for a very rough first estimate of Rr, but it would be risky above Fn = 0.3 (SLR = 1.0) and if the humps and hollows shape of the drag curve were important.

Regards,

Don MacPherson
HydroComp, Inc.