Propeller vibration in outboard engines is often the result of the propeller blades passing behind the gear case and skeg. The flow of water into the propeller blade is altered by the upstream obstruction, and the blade operates in the shadow of this obstruction. This causes a change in the blade loading onto the propeller shaft and on the engine, resulting in a small change in the instantaneous rotation speed, and this is felt as vibration.
The vibration created by the blade shadowing is related to the propeller shaft rotation speed and the number of blades on the propeller. To put some numbers to the frequency of the propeller blades being shadowed, here are two examples.
First, we assume the vibration occurs at an engine speed of 1,000-RPM. Next we apply the reduction gear ratio to find the propeller shaft RPM. For a 90-HP engine the gear ratio would typically be 2:1. This means the propeller shaft rotation speed will be 500-RPM.
If the propeller has three blades, then there are six occurrences of a shadowing for each shaft revolution, or 6-shadows-per-revolution x 500-RPM = 3,000-shadow cycles-per-minute.
The frequency of sounds or vibrations are typically expressed in cycles-per-second, so we have to convert cycles-per-minute to cycles-per-second; we divide 3,000 by 60 to get 50-cycles-per-second or 50-Hz.
Let us suppose the propeller is changed to a four-bladed design. We repeat the calculation. For four blades there are four occurrences of a blade shadowing for each shaft revolution, so we get 4-shadowings-per-revolution x 500-RPM = 2000 shadow cycles-per-minutes. Converting to per-second we get the frequency of the shadowing to be 2000 divided by 60 = 33.3-cycles-per-second. Recall because two blades are shadowed at once, the amplitude of the shadowing effect on instantaneous engine speed may be stronger, producing a stronger vibration. On the other hand, with a four-bladed propeller the frequency is changed to 33.3-Hz from 50-Hz, and if the boat hull and attached devices do not resonate at the new, lower frequency of 33.3-Hz then the coupling of the engine vibration into the hull and attached accessories may not be as strong.
There is no magic in the four-blade design; it is just going to change the excitation frequency of the engine vibration to be lower than the three-blade propeller would produce. This may or may not improve the sensation of vibration felt by passengers in the boat.
ASIDE: back in the 1930's there was an unofficial competition among Atlantic Ocean liners sailing from Europe to New York for the fastest trip time. The French Line built the fabulous liner NORMANDIE. The ship had four propeller shafts and enormous horsepower, 200,000-SHP at maximum power. The initial sea trials revealed a significant vibration in the stern portion of the hull at high speed, induced from the propellers and the shape of the propeller shaft bushings just ahead of the propellers. The ship sailed briefly with paying passengers, but complaints about the vibration in accommodations towards the stern were common. The ship was modified by adding additional stiffness to the hull structure in the stern, re-working the propeller shaft bushings, and changing all four propellers to four-blades from three-blades.
A sea triall following this refit resulted in an enormous reduction in vibration. But, unfortunately, a bigger problem was soon discovered upon return to port. A diver was sent down to inspect the propellers; upon coming back aboard, he reported all three propellers were in excellent condition. This report was unbelievable, and a second diver, a member of the ship's company, was sent to reinspect the propellers. His report was the same: only three propellers were attached. The inboard port propeller was missing.
NORMANDIE could not sail in this condition, so the inboard starboard propeller was removed, and the two three-bladed original propellers were reinstalled on the inboard shafts. The outcome of this not a good cure to the problem: the vibration was now worse than the original situation. The lost four-blade propeller was never found or recovered. Eventually, a second set of four-bladed propellers was ordered and installed, and NORMANDIE sailed with those propellers for the remainder of her service life.