RPM
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Not quite sure what you mean there, do you mean max static RPM? That isn't affected by weight nor is the RPM at take off (other than your take off speed and thus RPM may vary according to weight) , assuming you have a fixed pitch prop.
For a fixed pitch prop, at the same density altitude and airspeed profile, RPM at any given point in the climb profile should be the same, irrespective of weight.
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Fixed pitch. If on T/O you normally get, say 2400rpm. Then if you are carrying pax and full tanks, could the extra weight restrict the rpm a bit or is any reduction indicative of a possible fault? Again assuming similar atmospherics etc.
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The static RPM will vary with atmospheric conditions, but not weight. Any reduction in the static RPM for the same conditions would indicate a fault. When you line up, you should apply full power against the brakes, and note the figure you get. The more you get used to what the figure should be, the more chance you'll spot a fault.
The RPM at the point where you actually get airbourne may vary with weight. A heavier aircraft will get airbourne at a greater airspeed. This in turn will lead to a higher RPM. Think back to Ex 4, effects of airspeed on RPM.
In reality the difference in the RPM with the likely variable range of weights will be very small and difficult to notice, especially during such a critical phase of flight where you will be more interested in keeping the thing straight and establishing the correct airspeed.
The RPM at the point where you actually get airbourne may vary with weight. A heavier aircraft will get airbourne at a greater airspeed. This in turn will lead to a higher RPM. Think back to Ex 4, effects of airspeed on RPM.
In reality the difference in the RPM with the likely variable range of weights will be very small and difficult to notice, especially during such a critical phase of flight where you will be more interested in keeping the thing straight and establishing the correct airspeed.
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Again it depends on what you mean by take off, are you really watching the RPM at a critical point in flight? I check RPM and t's and p's when rolling but not again until well established in the climb. RPM depends on so many things, temperature, density altitude etc.
I teach that for a normal takeoff the brakes are released and full throttle should be smoothly applied with the throttle taking 2 to 3 seconds to reach the full power stop. At this point check the RPM guage to ensure that the RPM is indicating within the static RPM range and oil/temp pressure and fuel press (if applicable) are in the green arcs.
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The other thing to note is that static RPM (full power against the brakes) is dependent on the headwind. If you have a 20 knot headwind you will see a higher RPM compared to the nil wind situation.