In aeronautics and marine hydrodynamics, the advance ratio at which a propeller is operating is the ratio between the distance the propeller moves forward through the fluid during one revolution, and the diameter of the propeller. When a propeller-driven vehicle is moving at high speed relative to the fluid the advance ratio of its propeller(s) is a high number; and when it is moving at low speed the advance ratio is a low number. The advance ratio of a propeller is analogous to the angle of attack of an airfoil.
The fluid velocity relative to the propeller blade increases with distance from the hub, due to the rotational velocity of the propeller. Therefore, the direction of the flow relative to the propeller blade is equal to the vector sum of the speed of advance and the rotational speed of the propeller.
Comment:
It would appear that imagery of a propeller from which the diameter and the "angle of attack" can be determined
can be used to determine a turns-per knot (TPK) value, and, conversely, if the TPK and the diameter are known, the
angle of attack (pitch?) can be derived.
If these relationships can be so exploited, it may - repeat may - be possible to estimate TPK values from imagery alone.
If the suggested approach is valid, it might be possible to get a value before
the item of interest entered the water for the first time and from that you
could possibly derive other information of even greater value because of
empiric relationships that exist among those characteristics/capabilities.
Someone should investigate this possibility and I no longer am that person.
.
Bruce
TPK is not a linear function. Submarine propellers are designed to most efficient at maximum speed. Data collected on the same hull on the same day indicates TPK values of 9.54 at 26.06 knots, 9.61 at 14.1 knots and 10.25 at 8.08 knots.
At speeds below about five knots - and especially at speeds as low as 2-3 knots, TPK values will "decay"
significantly. Although none were derived at such speeds for the above case, other data indicates TPK values as high as 12-15 may have applied for that hull at 2-3 knots. I don't think you will find many submarine COs pleased to have to operate at speeds lower than or as low as three knots.
The battle about linearity was fought - and won - against the US submarine community many years ago; however, the results probably are still not well known, i.e., most will tell you TPK is linear, i.e., does not change as a function of speed. That assessment was the result of not being able to measure speed with the accuracy required to identify variations such as those noted above.
Thanks Bruce. I am very familiar with computing TPK. I had a Large Yacht for years and the curve was BRUTAL at WOT. The hull problem is much different with a submarine. Thanks for your posts.
