First of all, welcome!
Power/Thrust/Climb Angle/Climb Rate. All interesting and interlinked concepts when it comes to performance.
In simple terms, for a jet:
The engine produces Thrust, as a function of fuel flow and altitude. This ‘thrust available’ is pretty constant with speed.
For a given speed, there will be a certain Thrust required, to overcome the drag.
The drag and therefore the Thrust required will be at a minimum at a certain speed.
Any excess Thrust can be used to climb.
It follows, therefore, that the best angle of Climb will be achieved at the speed for minimum drag, using maximum Thrust.
If one knows the drag at any speed, and also knows the maximum thrust available, the angle of climb can be calculated geometrically. The problem for pilots is that we generally don’t know these values directly.
SID gradients are normally published as percentages, which is equivalent to an angle of climb.
Chart producers normally convert this angle to a rate, giving different values for different speeds.
Pilots will know the speed that they are going to use to fly the SID and can therefore read off the rate required.
Airplane Flight Manuals will publish rates of climb for given circumstances, so a comparison can be made with what is required, against what is achievable.
Now, when it comes to rate of climb, the deciding factor is excess power, not thrust. What is ‘excess power’?
Simply put, it is the power available from the engine, minus the power required for level flight.
But a jet engine produces Thrust, not Power!
We can resolve this dilemma by remembering that Power is equal to Thrust multiplied by Speed (using compatible units).
So, if we plot the available thrust (which is a function of fuel flow and altitude) against increasing speed, we will see that the Power available increases geometrically with increasing speed.
The Power required at various speeds will follow a similar shape to the drag curve.
The will be a range of speeds where the two curves are almost parallel. This means that we can get close to the maximum rate of climb from a jet aircraft over a wide range of speeds, although these speeds will become closer as you gain altitude.
All of these concepts are much easier to understand using graphs and diagrams, but my computer skills don’t run to that!
Try googling “Airplane Thrust required” and/or “Airplane Power required” but keep in mind that graphs for Piston engines will have some differences compared to those for jets.
To try to answer your specific question about the OPT: Airlines have Performance Engineers that will look at all the SIDS that are likely to be used and will check to see if the required gradients can be achieved.
if not, they will either prohibit that SID from being used, or they will publish an alternative route, called an “emergency turn” or “Engine-out SID”.