How many rapid-fire powerups are effective in Jazz Jackrabbit?
Up to 10 rapid-fires are useful
With ten rapid-fires Jazz shoots a bit over twice as frequently as with one. Additional powerups do not increase the speed any further. Each powerup decreases the time until the next shot, but does not affect the speed the shot moves at.
To establish this, I recorded myself firing from the same position with up to 16 rapid-fires and measured the rate of fire. The first twelve can be seen below - on the left, animated (though now decoupled from real time), and on the right a still image showing at least two shots with each level of powerup.
With one rapid-fire, Jazz fires about 3¾ times a second, and with ten, about 8.6 times a second. Each powerup you collect up to the limit makes each blaster shot a constant 8 pixels closer to the next (half a blaster width/per-frame delta).
No further improvement occurs after the tenth powerup, with the same spacing and firing speed. This is also what the GUNHED cheat code gives you.
Each powerup is more valuable than the last
The more rapid-fire powerups you've already collected, the bigger the increase in firing speed of the next one is (up to the limit). That's because the constant 8-pixel difference from each one is much more significant when the previous interval was 44px than when it was 100px.
The gap between shots with a single powerup is 108px, and for 10 and above is 36px. There is about a 5% increase in firing rate between 1 and 2, and more like 15% between 9 and 10. I counted the number of shots in a ten-second or longer window to produce the table below. The improvement is to shots per second.
| RF | Gap (px) | shots/s | Approx. improvement |
|---|---|---|---|
| 1 | 108 | 3.8 | ∞ |
| 2 | 100 | 4.0 | 5.3% |
| 3 | 92 | 4.3 | 7.5% |
| 4 | 84 | 4.6 | 7.0% |
| 5 | 76 | 5.0 | 8.6% |
| 6 | 68 | 5.5 | 10.0% |
| 7 | 60 | 6.0 | 9.1% |
| 8 | 52 | 6.7 | 11.7% |
| 9 | 44 | 7.5 | 11.9% |
| 10 | 36 | 8.6 | 14.7% |
| 11 | 36 | 8.6 | 0.0% |
A single shot still makes a big difference here, so the percentages are a bit noisy, but the overall trend is there. A longer measurement window would be more accurate, particularly after going through video recording and playback.
Higher numbers of powerups do not have any further effect on firing speed, up to the 16 I measured. Other weapons appear to be affected in the same way (other than TNT), but it's a lot harder to get measurements on those.