The aircraft can climb from steady level flight only if there is more available power than power required to fly level. This implies acceleration. All our discussion so far has involved steady (or non accelerating flight). The climb calculations are designed to support this assumption.
In reality as the aircraft climbs or gains altitude the density changes. As density changes we have learnt that the level flight speed will change. Typically the pilot would like to climb at constant speed. Note: another issue is the should the pilot be concerned with climbing at constant indicated airspeed or constant true airspeed.
To avoid such detailed analysis in the preliminary design stage, the assumption of equilibrium climb (no acceleration)is used. This is also referred to as quasi-steady climb. This means climbing at steady speed over an interval. To climb there must a vertical component of the speed. This means that the flight path inclination angle (γ)can not be zero.
From the power available curve and the power required curve above, for each altitude it is possible to calculate the maximum rate of climb (R/C)max , This maximum rate of climb takes place at a certain speed - V (R/C)max.
The analysis above can be repeated for several altitudes starting at sea level (SL) and extending to much beyond the cruise altitude
The assumption in these calculations is that the speeds computed are the true air speeds. The pilot however will find it convenient to climb at a constant indicated airspeed. If he does that, the true air speed would increase as he climbs - which implies that the climb is being accomplished with acceleration.
This illustration is a for a piston engine. You would calculate using thrust for a jet engine.