Blackdog_kt has made an excellent post.
I haven't bought CoD
yet so one quick question before I get carried away in the discussion - are the propellors on the 109 (and all the other aircraft for that matter) controlled by Constant Speed Units OR are they just variable pitch propellors?
The difference being, after takeoff you have reduced your throttle setting and RPM to the recommended settings and accelerated to the recommended climb speed:
With a Constant Speed Propellor - if you vary your throttle setting up or down and/or change your attitude by pitching up or down (within reasonable speed and power settings) the engine will maintain the RPM you have set.
With a Variable Speed Propellor - if you do the above - the RPM will either increase or decrease from what you have set at the change of power and/or the change of speed.
(the Variable Speed Propellor requires a lot more work/attention from the pilot than the Constant Speed Propellor btw)
Next - because I haven't bought the game yet - I do not know how accurate the Simulation is but I think I can speak in general terms and offer some insight (I hope).
To determine how much Power (measured in Horsepower or NewtonMeters etc) the engine can develop you have to know the RPM and the throttle setting - the throttle setting on the '109 and most WWII aircraft is a measure of the Intake Manifold Pressure and on the '109 is measured in Atm - Atmospheres, I believe. (On the USA aircraft it is measured in Inches of Mercury).
On a `normally aspirated engine' - No Supercharger/Turbocharger - the maximum manifold pressure you could get - at ground level would be local atmospheric pressure -
about 1 Atm or 30 Inches.
But most engines we will see in CoD are supercharged. (not the Tiger Moth

) Therefore we can get throttle settings (power settings - manifold pressures) of 1.5 Atm or 45 Inches of Hg etc.
Engine Manufacturers set limits on their engines - for reliability and engine life. These Limits are specified in maximum RPM and maximum Manifold Pressure. As well, for HIGH power settings, like Takeoff Power, there may be a time limit.
RPM limits are set so the engine stresses do not cause the engine to `fly apart' and Manifold pressures limits are observed so that the HEAT from combustion does not heat the engine to the point that the metal of the combustion chambers and pistons are weakened by the high temperatures to the point of failure.
On some engines there may be another HIGH power setting that has no time limit - less than Takeoff Power - and in North American Engines called METO - Maximum Except Take Off.
On Take Off different aircraft with different engines have different procedures for setting Takeoff Power.
Usually the Prop control is set to Maximum RPM or Full Fine.
The throttle is carefully brought up to the maximum Manifold Pressure specified (OR another controller automatically limits the Manifold Pressure to the maximum so all the pilot has to do is `firewall' the throttle - set it to `wide open')
The propellor and its controls are adjusted/set by the manufacturer and mechanics so that on Takeoff the engine will achieve - but not exceed - its maximum rated RPM. This RPM is usually
governed so that the pilot can concentrate on the takeoff and not have to adjust the engine RPM down in the middle of the takeoff roll as his speed increases.
So we have taken off and reduced throttle settings (manifold pressures) and RPM to suitable values for the phase of flight.
Lets say we are cruising along at typical long range cruise values. Relatively low RPM has been set. refer to Blackdog_kt's excellent post.
Up ahead we spot co-altitude bogeys that are probably hostile so we want to increase our speed and energy state ( and climb). So to accelerate and/or climb we need MORE POWER. How do we get more power? By burning MORE fuel-air mixture. So we push the throttle up to the maximum value allowed! (on a constant speed prop the propellor will coarsen to maintain the set RPM - on a variable pitch prop the RPM will increase)
And we start to accelerate slowly/climb slowly. Not good enough! We need more power. How do we burn more fuel-air mixture? How do we increase the number of power strokes in the engine per minute when we are already at the Maximum Manifold Pressure? We INCREASE the RPM.
So, to accelerate from a steady speed we need more power (more force to appy to the mass to get the acceleration). We get that power by realising that power output is controlled by how much fuel we are burning and that is a function of RPM and Throttle setting (manifold pressure). Therefore we set - in this case - the maximum power setting allowed for this phase of flight - RPM and Manifold Pressure - maybe even going to the point of War Emergency Power.
When we don't need full power and want to conserve our limited fuel supply we choose a power setting with an efficient propellor setting - RPM - to get the best speed at that power (throttle setting).
Hope this adds to the discussion.