Calculating Ship's Engine RPM To Arrive On Time

You must average 16.25 knots to reach port at a designated time. Your propeller has a pitch of 21' 08", and you estimate 4% negative slip. How many RPM's must you average to arrive on time?

Given:

S.O.A = 16.25 kts
 Pitch = 21' 08"    (8 inch x 1 foot    = 8 ft   = 0.66 ft)
          = 21.66 ft                 12 inch      12
   Slip = - 4%

What is asked?

Average revolution per minute (RPM)

Solution:

1. We have to get first the value of efficiency.

                 efficiency = 100 - (-4)   
                                         100
                                 = 100 + 4
                                       100
                                 = 104 
                                     100
                            Eff = 1.04

2. To solve for RPM, we have to use the formula for S.O.A. and then cross multiply to derive the formula for the revolution per minute.

                    S.O.A = RPM x P x 60 x Eff
                                            6080                (We have to cross multiply)
 RPM x P x 60 x Eff = S.O.A x 6080

 RPM x P x 60 x Eff = S.O.A x 6080
             P x 60 x Eff    P x 60 x Eff

 RPM x P x 60 x Eff = S.O.A x 6080
             P x 60 x Eff    P x 60 x Eff          (Do some cancellation)

                      RPM = S.O.A x 6080
                                    P x 60 x Eff

                               = 16.25 x 6080         
                                    21.66 x 60 x 1.04

                               =  98800    
                                    1351.58

                      RPM = 73

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