If an aircraft wants to fly at a fixed cruise speed, will the rate of climb have any effect on that? For example, let's assume an aircraft has to fly at a cruise speed of 0.8 Mach. How will the rate of climb be determined so that the aircraft can cruise at that altitude after gaining the altitude at which it is desired to cruise?
The only way that rate of climb and cruise are related is through the horsepower rating of the engine. A more powerful engine will furnish the greater rate of climb and the higher cruising speed.
However, note that the horsepower requirement to maintain a given cruise scales as the third power of airspeed. So while adding ~20 horsepower to a 100HP engine will provide a significant improvement in rate of climb, the resulting increase in cruising speed will be small.
Does cruise speed depends on rate of climb?
Yes, cruise speed, rate of climb and altitude are related among each other due to the fact that both to fly horizontally and to gain altitude you need the power from the engine(s) and everything depends on the altitude.
In particular, on one side your airplane:
- needs power to win the aerodynamic drag and the inertia in order to maintain or gain horizontal speed; aerodynamic drag depends on air density i.e. altitude;
- it also needs power when climbing.
On the other side, the power supplied by the engine(s) must compensate for the sum of 1. and 2. and it depends on altitude and speed.
So for example if at a given altitude the whole power from the engine(s) is used to fly as fast as possible then there's no power left to climb and the rate of climb is simply zero. If at another condition the airplane is both flying fast and gaining altitude using again the whole power available, then there's no room to fly faster nor to climb faster; if a faster climb is needed in this condition, then the cruise speed must be reduced in order to trade a bit of power to gain altitude; and viceversa. Obviously if the airplane is flying at a certain speed without using the whole power available then it has room both to fly faster and/or gain altitude, anyway always within the limitation of the available power at that particular speed and altitude.