Pneumatic Golf Ball Launcher Designer

Design and optimize your pneumatic launcher with real physics calculations

0 ft
Max Distance

Trajectory

0
Flight Time (s)
0
Max Height (ft)
0
Range No Spin (ft)
0
Range With Spin (ft)
ft
Launch
Barrel
Chamber
Spin

Calculated Results

Muzzle Velocity
0 ft/s
Maximum Distance
0 ft
Time in Barrel
0 ms
Flight Time
0 s
Max Height
0 ft
Exit Pressure
0 psi
Muzzle Energy
0 J
Chamber:Barrel
0 :1
Seal Efficiency
0 %
Exit Acceleration
0 g

Projectile : Golf Ball

▼
TypeDiameterMassCd
Golf Ball42.67 mm45.93 g0.24
Tennis Ball66 mm57 g0.50
Ping Pong40 mm2.7 g0.50
Nerf Dart13 mm1.0 g0.40

Barrel : 1.5" x 36"

▼
36"
6" 72"
Golf Ball Fit: SDR 21 @ 1.5" has 1.720" ID - provides ~0.040" clearance for a 1.680" golf ball. Ideal for minimal friction while maintaining air seal.
Seal Efficiency: 95% — Excellent seal with minimal blow-by

Chamber : 2" x 24"

▼
24"
6" 48"
80
20 150

Valve : QEV 1/2"

▼
Valve TypeSizeCvOpen Time
QEV1/4"0.10<5 ms
QEV3/8"0.80<5 ms
QEV1/2"3.25<5 ms
QEV3/4"5.50<5 ms
QEV1"8.00<5 ms
Sprinkler (mod)3/4"2.00*~20 ms
Sprinkler (mod)1"3.50*~20 ms

* Sprinkler Cv values are effective values accounting for internal flow restrictions

Barrel Curve & Spin : 0 RPM

▼
0" (straight)
0 6"
36" (full)
6" 36"
0.35
0.1 (slick) 0.8 (grippy)
2000
0 5000
Magnus Effect: Backspin creates lift force that extends flight distance. Higher spin = more lift, but also more drag.

Optimization : Zero Exit Accel

▼
Goal: Zero Exit Acceleration
For maximum efficiency, the projectile should exit when chamber pressure equals atmospheric (~14.7 psi). This means all stored energy has been transferred to the projectile with no wasted pressure.
Optimize Barrel

Adjusts barrel length so the expanding air reaches atmospheric pressure exactly when the ball exits. Longer barrel = more time for air to expand = lower exit pressure.

Optimize Chamber

Adjusts chamber volume to match your barrel. Larger chamber = more air = more energy, but requires finding the right balance for zero exit pressure.

Note: These calculations assume isothermal expansion (slow process). Real launches are closer to adiabatic (fast), which is less efficient. Results are theoretical maximums - actual performance will be somewhat lower.

Valve Flow Comparison

Flow rate comparison at different pressure differentials. QEVs provide significantly faster flow due to larger effective orifice and minimal internal restrictions.

Pressure vs. Velocity

Velocity increases roughly with square root of pressure. Current operating point shown in red.

PVC Pipe Reference Data

Nominal Size OD (in) ID (in) Wall (in) Pressure (psi) Projectile Fit

Physics Reference

Core Equations

Exit Pressure:
Pexit = P0 × Vch / (Vch + Vbar)

Muzzle Velocity:
v = √(2E / m)

Where:
P0 = initial pressure (psi)
Vch = chamber volume
Vbar = barrel volume
E = muzzle energy (J)
m = projectile mass (kg)

Magnus Lift Force

Lift Force:
FL = ½ × CL × ρ × A × v²

Spin Factor:
S = ω × r / v

Where:
CL = lift coefficient ≈ 0.5 × S
ρ = air density (1.225 kg/m³)
A = cross-sectional area
ω = angular velocity (rad/s)
r = ball radius (m)

Valve Flow

Volume Flow Rate (SCFM):
Q = Cv × √(ΔP × P2 / (T × SG))

Where:
Cv = flow coefficient
ΔP = pressure differential (psi)
P2 = downstream pressure
T = temperature (°R)
SG = specific gravity (1.0 for air)

Trajectory

Drag Force:
FD = ½ × Cd × ρ × A × v²

Where:
Cd = drag coefficient
ρ = air density (1.225 kg/m³)
A = cross-sectional area (m²)
v = velocity (m/s)

Optimal angle: 30-40° with drag

Blow-by / Seal Efficiency

Gap Ratio:
rgap = (Abar - Aproj) / Aproj

Base Efficiency:
ηbase = e-2.0 × rgap

Dynamic Penalty:
tf = √(100 / P)
ηdyn = e-3.0 × rgap × (tf - 1)

Where:
Abar = barrel cross-section
Aproj = projectile cross-section
P = operating pressure (psi)
η = ηbase × ηdyn (total)

Muzzle Energy

Average Pressure:
Pavg = (P0 + Pexit) / 2

Muzzle Energy:
E = Pavg × Aproj × L × η

Where:
Pavg = average pressure (Pa)
Aproj = projectile area (m²)
L = barrel length (m)
η = seal efficiency (0-1)