Hi Steve,
For the new tug fuel usage formula:
Engine Power Used = ((Ship Size + Towed Size) / Ship Size) x (Current Speed / Max Speed).
Do the tow's engines contribute to CurrentSpeed? In other words, is the formula for MaxCurrentSpeed something other than
MaxCurrentSpeed = ShipSize*MaxSpeed/(ShipSize + TowedSize)?
If the answer is "yes", then I think there's still a problem, since the tug will be paying fuel costs for both its engine power and the tow's engine power. (I'm assuming here that "Max Speed" is the max speed of the tug when it's not towing anything.) If the tow's engines contribute, then I think the formulae should be:
MaxCurrentSpeed = (ShipSize*MaxShipSpeed + TowedSize*MaxTowedSpeed)/(ShipSize+TowedSize)
FuelUsageRate = MaxFuelUsageRate*(CurrentSpeed/MaxCurrentSpeed).
Note that I used "MaxFuelUsageRate to get the units right - the formula you gave is actually a (dimensionless) ratio. This is easy to see if you set TowedSize=0 and CurrentSpeed=MaxSpeed; "Engine Power Used" becomes 1, which is probably not what you're intending
John