When shot upwards:

max. height = 0.5 * v * v / g | Example: at 36 Km/hour (10 m/s), this gives max height=0.5*10*10/9.8=5.1 meter. |

time of flight = 2 * v / g | Example: at 36 Km/hour (10 m/s), this gives time of flight=2.04 seconds |

launch velocity = 0.5 * g * (time of flight) | Example: 5 seconds time of flight gives 24.5 m/s (88 Km/hour) |

launch velocity = square root (2 * g * height) | Example: 10 meter height gives 14 m/s (50 Km/h) |

range = 0 |

When shot at a 45 degree angle:

max. height = 0.25 * v * v / g | Example: at 36 Km/hour (10 m/s), this gives max height=0.25*10*10/9.8=2.5 meter. |

time of flight = 1.41 * v / g | Example: at 36 Km/hour (10 m/s), this gives time of flight=1.44 seconds |

launch velocity = square root ( g * range ) | Examle: if range=35 m, velocity=18.5 m/s (67 Km/h) |

launch velocity = 0.71 * g * (time of flight) | Example: 5 seconds time of flight gives 34.6 m/s (124 Km/hour) |

launch velocity = 2 * square root ( g * max height) | Example: 10 meter height gives 19.8 m/s (71 Km/h) |

range = v * v / g or 4 * max. height | Example: 100 Km/h (27.8 m/s) gives a range of 79 meter |

range = 0.5 * (time of flight)^{2} |
Example: 5.5 sec flight time gives a range of 148 meter. Warning: mind the air resistance |

v=velocity

g=gravity (between 9.78 and 9.83 m/s

Additional formula:

1 m/s=3.6 Km/hour

1 m/s=3.281 feet/second=2.24 miles/hour

Energy = force * distance = mass * g * height = 0.5 * mass * v * v

Note that all of the above formulas are irrespective of the units you use; put feet and pounds in and you get feet and pounds out.

The small onager that I build

The onager simulator

A full computer simulation of the onager

Measure 4 Measure

All unit conversions you will ever need.

(c) , , 16 Apr 2001