Yes, there are many variables and one of the key decisions when designing a pulsejet is establishing the speed at which maximum thrust will be generated. If you design an engine for maximum static thrust then the ram-effect will soon cause problems once you get any decent amount of speed on.
For example, the Argus engine used in the V1 flying bomb was said to produce about 500-600lbs of static thrust but at the V1's designed flying speed (around 360-380mph) the thrust increased to about 900lbs. This was achieved by the use of a carefully designed diffuser on the intake.
Airframe considerations are also very important. Structural integrity is one of the biggest problems -- mass balancing of control surfaces and ensuring that the combination of airframe stiffness and mass don't combine to produce unwanted resonances that can create levels of flutter that produce structural failure at certain speeds.
You can do "so much" with a calculator but eventually it comes down to refinement by empirical means -- that's where the fun begins
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