Norrhin 



gX" = I.-' . IT^U^ + T;u„'+ L • iT,"„,„ [n|n + L • iT„>^ 



(q!" - QV)A = L-'g • Ql\ + L-^^g*'^^ . Q^" • n . L-'g • Q^"^ (7.6) 



+ L-' . iQ:„u2 + L-'Q;„un + iQ['„,„ |n|n + iQ>^ 



with 



i^:, =-^^ • (i - w)'. iK etc. 



The steady-state hydrodynamic thrust and torque are given 

 as functions of forward speed, u, and rate of revolutions, n, based 

 on open water K_ and K. characteristics; K^ and Kq are first 

 approximated by square functions of J = (u/iD)(i - w) or l/j. 

 (Note that a linearization of these characteristics does not result 

 in a linearization of the (u,n)-dependence. ) The Nordstrom data 

 [ 70] may be used when reversing or transient maneuvers are con- 

 sidered. In general it is then necessary to confine the analytical 

 functions to limited ranges of propeller advance coefficients, i.e. 

 to use alternative coefficients as in Eq. (7.2). Harvald has presented 

 useful infornnation on the propulsive factors at arbitrary steady-state 

 advance conditions, [ 71] . The effects of separating boundary layer 

 flow along the stern of a retarding ship are still less predictable. 



The added mass and moment of inertia involved in unsteady 

 maneuvering of the propeller are functions of the momentaneous 

 advance coefficients as well as of the rate of change of r.p.m. In 

 small changes from normal propulsive conditions the added inertia 

 is small as blade angles of attack are small. Naval architects often 

 use a value of 30 per cent of rigid screw inertia for the added inertia; 

 although this figure originates from model tests with screws oscil- 

 lating at zero advance coefficient it may still be used as an effective 

 average value during the short reversing stage of an engine maneuver. 

 In fact this stage is dominated by the large control torques and by the 

 way they are used. 



When simulating maneuvers with diesel-powered ships it 

 shall be observed that normal r.p.m. control is not possible for n 

 less than some 35 - 40 per cent of design shaft speed n^. The torque 

 delivered is here rapidly reduced, mainly due to loss of charge air 

 pressure. (For high r.p.m, Q^ is almost zero.) Slow speed 

 maneuvering must be performed by intermittent use of the propeller, 

 which requires repeated starting of the engine. Reversing maneuvers 

 must await drop of speed to some 60 per cent of the full speed value, 

 at which lower speed braking air may be applied. There is also a 



862 



