Explore how contact height, speed, position, aim, air resistance and spin change a 100 mph first serve. The launch direction is solved to land exactly on your selected target.
IN · clears net
Net clearance?
Gap between the bottom of the ball and the net at crossing. Positive clears; negative hits the net. This is not a serve-in percentage.
Landing point?
The target you selected. Launch elevation and sideways aim are solved to reach it; the model does not simulate random serving error.
Box margin?
Distance from the selected target to its nearest service-box boundary. Larger margin leaves more room for error, but does not quantify your consistency.
Flight time?
Time from racket contact to first ground contact. Playback can continue through an illustrative rebound.
Launch angle?
Calculated elevation needed to hit your target. A negative value means the ball leaves the racket downward.
Speed at bounce?
Speed just before first ground contact, after any air resistance. It is not the rebound speed.
Trajectory · side elevation
Vertical scale enlarged for readability
model pathno-dragnetrebound estimate
0 ms
contactnet · first bounceend of rebound
Placement · top view
Receiving backcourt shown at half depth · singles serve
Live spin inspector
Ball rotation, spin axis and racket contact
server view · launch spin · 3D axis
Server view (racket side) · no spin selected.
Total spin0RPM0.0 rotations/sec
Combined spinFlat / no spinaxis inactive
Vertical component
0 rpm
Side component
0 rpm
Longitudinal component
0 rpm
Illustrative brushing directionNo brush selected
The arrow shows rear-face brushing implied by topspin and sidespin, not an exact contact patch. Clock positions are approximate. Longitudinal spin needs out-of-plane contact geometry; a 2D arrow cannot specify it.
Three transparent force layers
Geometry applies gravity. Air resistance adds quadratic drag. Spin adds 3D Magnus force from the selected RPM vector. The numerical solver adjusts both elevation and sideways aim to preserve your target. Assumptions: 57.7 g, 67 mm ball and air density 1.225 kg/m³.
Fdrag = ½ρCdAv² · FMagnus = ½ρACLv² · S = rω⊥/v
Running checks…
What remains simplified
Fixed 3D spin vector within each flight segment; spin changes at bounce
CL = min(0.35, 0.60 × spin ratio) as a working approximation
No spin-dependent change to the separate drag setting
Rotating seam uses a smooth spherical dog-bone approximation; felt flecks are visual only
No wind, ball deformation or line-call tolerances
Bounce estimate: rigid thin-shell ball, restitution 0.75, friction coefficient 0.55. Friction opposes contact slip, capped by the normal impulse, and changes both speed and spin. These are illustrative parameters, not calibrated to a court surface. Rebound ends at the receiving baseline or second bounce. Vertical-axis sidespin alone does not give a sideways impact impulse.
Net clearance uses the bottom of the ball, including its 3.35 cm radius. Net height uses a labelled parabolic sag approximation from 0.914 m at centre to 1.07 m at the singles sidelines.
Court constants: 23.77 m baseline-to-baseline, 8.23 m singles width, 6.40 m net-to-service-line. Spin presets are illustrative, and all measurements are analytical estimates rather than coaching or officiating data.
Serve Lab