Jump Timing Window
Run and jump, plus the finding: the timing window gets WIDER as you speed up, so an endless runner does not get harder because of the jump.
Space, up arrow or a click jumps. The green band on the ground is the window — every position inside it clears the obstacle ahead, and nothing outside it does. Change the speed and watch the band get wider. Nothing is uploaded.
Running faster makes the jump easier
The arc is a parabola and never changes; what decides whether a jump is possible is the window. The arc stays above an obstacle of height h for a fixed time, the obstacle takes w/s to cross, and the window is the difference: (u₂ − u₁) − w/s. The whole of the interesting behaviour is in that second term — and it shrinks as you speed up.
| Obstacle height | 300 px/s | 600 px/s | 1200 px/s | Ceiling |
|---|---|---|---|---|
| 40 px | 0.470 s | 0.570 s | 0.620 s | 0.670 s |
| 80 px | 0.337 s | 0.437 s | 0.487 s | 0.537 s |
| 120 px | 0.158 s | 0.258 s | 0.308 s | 0.358 s |
| 150 px | -0.108 s — impossible | -0.008 s — impossible | 0.042 s | 0.092 s |
Every row widens left to right. Read the last one: a 60 px obstacle 150 px tall is impossible at 300 px/s — the window is negative, meaning the crossing takes longer than the arc stays up — marginal at 600, and comfortable at 1200. Speeding up turns an impossible jump into an easy one.
The last column is where each row is heading. As speed rises the w/s term vanishes and the window climbs towards the time the arc spends above the obstacle — always approaching it, never reaching it. And it is never simply the hang time (0.78 s); that would mean an obstacle with no height and no width.
So an endless runner does not get harder because the jumps get tighter. They get looser. The difficulty is coming from how often obstacles arrive and how little warning you get — not from the jump.
What speed cannot fix
Height is the one thing running faster does not help with at all. The arc peaks at 152.1 px and nothing taller can be cleared at any speed whatever — the two crossings do not exist. At exactly the apex they coincide, so the window collapses to zero: an obstacle precisely apex-high needs an infinitely narrow jump.
| Height | Widest clearable at 300 px/s | Widest clearable at 600 px/s | Widest clearable at 1200 px/s |
|---|---|---|---|
| 40 px | 201 px | 402 px | 804 px |
| 80 px | 161 px | 322 px | 644 px |
| 120 px | 107 px | 215 px | 430 px |
| 150 px | 27 px | 55 px | 110 px |
Width, by contrast, scales exactly with speed — double the speed and you can clear an obstacle twice as wide, at every height. So of the two dimensions of an obstacle, speed buys you one of them completely and the other not at all.
The window is derived, and then found again by brute force — sweeping every launch position and walking the arc across the obstacle. The two agree to within 0.07 milliseconds, and a live check at 95 px and 750 px/s — neither of which appears in the tables — comes in at 0.03 ms.
How to use
- Press space, up arrow or click to jump.
- The green band on the ground is the window — every position in it clears.
- Change the run speed and watch the band get wider.
- Turn the window off to see how much harder it is without it.
- Press Run for a new course.
Frequently asked questions
What is the jump timing window?
The stretch of ground from which pressing jump clears the obstacle ahead. Press before it and you land short; press after it and you clip the front. It has a closed form: the time the arc spends above the obstacle, minus the time the obstacle takes to cross, which is its width divided by your speed.
Do jumps get tighter as an endless runner speeds up?
No — they get looser, which surprises almost everyone. The window is the time above minus width over speed, and that second term shrinks as you go faster. A 60 pixel obstacle 80 pixels tall gives a 0.337 second window at 300 px/s and 0.487 seconds at 1200.
Can speeding up make an impossible jump possible?
Yes, and it is the sharpest case. A 60 pixel obstacle 150 pixels tall has a negative window at 300 px/s — the crossing takes longer than the arc stays above it — so it cannot be cleared at all. At 1200 px/s the window is a comfortable 0.042 seconds.
Then why do endless runners get harder?
Not because of the jump. If the window widens with speed, the difficulty has to be coming from how often obstacles arrive and how little warning you get before one does — the reaction problem rather than the timing problem.
Is there anything speed cannot fix?
Height. The arc peaks at 152.1 pixels and nothing taller can be cleared at any speed whatever, because the two crossings do not exist. Width scales exactly with speed — double the speed and you clear an obstacle twice as wide — so of the two dimensions, speed buys you one completely and the other not at all.
How was the window checked?
Twice, deliberately. It is derived in closed form and then found again by brute force, sweeping every launch position and walking the arc across the obstacle. The two agree to within 0.07 milliseconds.
Does this send anything anywhere?
No. Every course is generated and every jump computed in your browser, and nothing is uploaded.
🔒 This tool runs entirely in your browser. Nothing you enter is uploaded, logged, or stored.