To be more specific if i have ship speeds of 3m/s , 6m/s , 9 m/s and maximum of 13 m/s , how can i relate these speed values to the propeller rpm so that the ship can be maneuver at those speeds.
Yes. You have to assume that water is an inelastic medium and that there is no propeller cavitation. With those assumptions, for a given value of pitch, forward speed of the ship is a direct function of propeller RPM. Naturally, those are idealized conditions! The faster you rotate the propeller, the higher the chances of cavitation, the less exact this derivation will be (ship will go slower than the derived equation suggests).
First we address propeller pitch. To define pitch angle, simplistically because in actual designs the ideal is never possible, a propeller with 0 pitch angle could be described as a disc. It rotates, but creates no thrust at all. A propeller with 90 degree pitch also creates no thrust, and has a difficult time to rotate at all. Because with 90 degree pitch, the blade surfaces are parallel to the shaft.
As you increase pitch angle from 0 degrees, a rotating propeller creates thrust in a direction perpendicular to rotation. Equation (1) below is derived in the sidebar. In brief, looking at the pitch angle Φ at a given radius from the shaft, and knowing that in one full rotation of the propeller, the blade must travel a distance of 2πr, or πd, you can determine that the motion created in one complete rotation of the propeller is:
distance moved in one prop rotation = π * d * tan(Φ) (1)
where the pitch angle Φ applies to blade pitch at a radius d/2 from the shaft, for a propeller of diameter d. (Usually the pitch of propeller blades is measured close to the tips of the blades. In real propellers, pitch will increase as the blade approaches the shaft, to prevent cavitation. At every radius point from the shaft, you want the propeller blade to push through the same amount of water.)
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To derive that equation, assume you are dragging a flat plane through water, at an angle from the direction in which it is being dragged. The distance dragged we'll call dd, and the perpendicular distance traveled, as water is pushing the plane sideways, we'll call dp.
tan(Φ) = dp / dd
dp = dd * tan(Φ)
Instead of a plane being dragged a linear distance dd, in a propeller, we have blades being dragged through the water a distance of πd for every rotation of the prop. Replace dd with πd, and you get the equation (1) above, for perpendicular distance moved in one full rotation of the propeller.
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Now let's introduce speed in this discussion.
Distance moved by ship = π * diam. * tan(Φ) for each rotation of propeller, which is equation (1). Therefore it follows,
Distance traveled per minute = π * diam. * tan(Φ) * RPM
Distance traveled per second = π * diam. * tan(Φ) * RPM / 60 (2)
where diam is propeller diameter, and Φ is blade pitch angle. So, if you want to estimate ship speed in m/sec, from prop RPM, in equation (2), you would express prop diameter in meters.
Note that ship size, engine power, hull speed, none of that figures in this estimate. All you need are the assumptions mentioned at the very beginning. Inelastic medium, which pretty well describes water, and no cavitation. To get no cavitation, the bigger the ship, the larger the prop will have to be.
Dear Mohamed,
you can use e.g. this tool as starting point: http://www.csgnetwork.com/marinepropcalc.html
B.R.,
Ari
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