A projectile does two independent things at the same time: it moves sideways at constant speed
(nothing pushes it horizontally) and it accelerates downward under gravity. Splitting the launch into
those two components — horizontal v·cosθ and vertical v·sinθ — is the whole trick.
Press launch to watch them combine into the familiar arc.
Throw a ball at 20 m/s and 45° from ground level. It flies for 2.9 s, peaks at 10.2 m, and lands 40.8 m away — and hits the ground at the same 20 m/s it left, just angled downward.
The neat result: on flat ground, 45° gives the maximum range, and any two angles that add to 90° (say 30° and 60°) land in the same spot.
Range depends on the product of horizontal speed and hang time. Lower angles have more horizontal speed but less hang time; higher angles the reverse. 45° balances them — on level ground. Launch from a height and the best angle drops below 45°.
Not here. Without air resistance, all projectiles follow the same path regardless of mass — a cannonball and a pebble launched identically land together. Add drag and that changes.
For dense, slow, heavy objects over short distances, barely. For light objects, high speeds, or long ranges, very — real range can be a fraction of the ideal. Treat this as the frictionless ideal.
Gravity is about ⅙ of Earth's, so the same throw goes roughly six times farther and stays up about 2.5× longer. Switch the gravity buttons to see it.
| Club | Ball speed | Launch | Backspin | Carry | Total | Apex |
|---|
A golf ball in flight is pushed by three forces: gravity, drag (opposing its motion through the air), and Magnus lift (the sideways/upward force from spin, the same effect that curves a soccer free kick or a spinning baseball). This simulator integrates all three numerically in 3D — downrange, height, and left/right curve — using RK4, the same verified integration method used elsewhere on this site. Backspin creates lift (holding the ball up and extending carry); tilt that spin axis off-vertical and the same effect pulls the ball sideways into a draw or fade.
A PGA Tour average driver swing — 167 mph ball speed, 10.9° launch, 2,545 rpm backspin — carries 267 yards in this model with no wind at sea level, matching published Tour averages closely, then adds another 3 yards from two real bounces and a short roll-out for a 270-yard total. Tilt the spin axis 20° and the same swing curves about 35–40 yards offline by landing — a real slice or hook, not a cosmetic bend.
Magnus lift fights gravity for longer, flattening the descent and extending the time the ball spends moving forward before it falls — up to a point. Too much spin (a "sky ball") adds height without adding distance, since the extra lift steepens the whole trajectory instead of extending it.
Grass gets trapped between the clubface and the ball at impact — the "flyer lie" — reducing the friction that normally imparts spin. Less backspin means less lift and a lower, longer-rolling, less controllable shot, which is exactly why rough is harder to stop on the green from.
Thinner air means less drag and less Magnus lift working on the ball — the classic "ball flies farther in Denver" effect. It also means slightly less lift, so very high-spin, high-altitude shots can fly a little flatter than expected even as they go farther overall.
Each bounce is a real, separately-integrated arc — vertical speed reflects off the surface at that surface's restitution (a lot of energy lost on sand or green, much less on hardpan), horizontal speed is cut by its friction, and the cascade repeats until the bounce height becomes genuinely negligible, followed by a decelerating roll-out. It's calibrated to realistic total distances, not a full contact-mechanics simulation — read individual bounce heights as illustrative, not laboratory measurements.
Every row recalculates under whatever conditions are currently set, using each club's own pro-average launch numbers — so the table always answers "how would each club do right now," not a fixed reference condition. If you've adjusted a club's own ball speed, launch or spin away from its pro average, the callout above the table compares your actual dialled-in shot to what a pro would get with that same club under those same conditions.
The Moon has no atmosphere at all — drag and Magnus lift both vanish entirely, wind is meaningless, and the ball follows a pure gravity-only arc at ⅙ Earth gravity (a real driver would sail for hundreds of yards). Mars keeps a thin CO₂ atmosphere — about 0.6% of Earth's sea-level pressure — so wind and altitude still matter, just far more weakly, on top of roughly ⅓ Earth's gravity.
Releases in which this page changed, newest last. Derived from the archived copy of every release, not from notes written afterwards — so it reflects what actually shipped. Site-wide passes are left out; they are in the full changelog.