9. Explain relationship between main engine power and resistance of ship’s hull?

We consider that effective thrust force (generated by propeller when a ship moves) is T (KG), in balance moving condition, we have:

T = R (KG)

To maintain ship’s speed at V (m/s) with resistance R (KG), necessary power can be determined: NK = TV/75 or NK = RV/75 (hp)

In fact, ship's hull has an effect on thrust force of propeller. That effect can be performed as hull efficiency hH :

hH = NK/ NP

Where:

- NK : Necessary power to maintain ship's speed at V (m/s), with resistance R (KG).

- NP : Thrust power of propeller. It is performed:

Np = TpVP/75(hp).

VP - Advance speed of propeller(m/s).

TP - Thrust force of propeller   (KG)

In fact, the propeller is now working in water, which has been disturbed by the passage of the hull, and in general the water around the stern has acquired a forward motion in the same direction as the ship. This forward-moving water is called the wake, and one of the results of the wake influence is that the propeller's speed is not the same with speed of the ship. The difference between ship and propeller's speed is called wake speed VW.

Vw=V-Vp(m/s).

According to Froude expression, wake coefficient w is defined as a ratio between wake speed and propeller's speed:

w=Vw/Vp or         w=(V-Vp)/Vp       

However, Froude expression is used only in older published data, particularly British.

According to Taylor definition, wake coefficient w is the ratio between wake speed and ship's speed:

w=Vw/V or w=(V-Vp)/V

          - For one propeller-ship:w = 0.5 d - 0.1

          - For two propellers-ship:w = 0.5 d - 0.16

          (d: Fat coefficient of the ship).

Then, propeller's speed is that:

VP = V(1-w)(m/s).

When a ship's hull is towed, there is an area of high pressure over the stern, which has a resultant forward component reducing the total resistance. However, with a self- propeller hull, the pressure over some of this area is reduced by the action of the propeller in accelerating the water flowing into it, the forward component is reduced, the resistance is increased and so also the necessary thrust force to propel the ship. Therefore, when propeller working to propel the ship only T (KG) overcome resistance R of ship and component (TP - T)(KG) overcome augment of resistance when accelerating the water.

Ratio: (Tp-T)/Tp=t is called thrust-deduction fraction. The thrust-deduction fraction t is determined by practical formula of Kenvil:

T=C1w

C1: coefficient depends on rudder structure characteristic. C1 = 0.5 ¸ 1.05.

We can perform:

Tp(1-t)=T (KG).

Then: Tp = T/(1-t) or Tp = R/(1-t) (KG).

Now, use determined values on formula of hull efficiency:

ηH = Nk/Np = (TV/75)/(TpVp/75)=TV/TpVp=RV/(R/(1-t).V.(1-w))

And: ηH = (1-t)/(1-w)

Thrust power of propeller:

Np = Nk/ ηH or Np = RV/75 ηH (hp)

Then, power on propeller hub:

Ncv=Np/ ηp (hp).

With hP is efficiency of propeller, for:

- Non-controllable pitch propeller:hP = 0.6 ¸ 0.75.

- Controllable - pitch propeller:hP = 0.58 ¸ 0.65.

When driving propeller, a part power output of a main engine is lost to overcome friction resistance on shaft bearings, clutch, and reducing gears box... So the power of a main engine depends on also shafting efficiency htr :

Ne = Ncv / ηtr =RV/75 ηH ηp ηtr (hp).

Shafting efficiency depends on characteristics of propulsion plant:

- Direct driving propulsion plant: htr = 0.95 ¸ 0.98.

- For indirect driving propulsion plant, shafting efficiency htr still depends on efficiency of clutch and reducing gears box and its value is about 0.86 ¸ 0.96.

In fact, the power of a main engine Ne determined above equals to only 85% its designed power.