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Aiming a hosepipe, intuition told me a 45-degree angle would maximise the distance travelled by the water, as it would for a projectile. But when I did this, the water actually went a shorter distance. Why? (continued)

Nick Canning
Coleraine, County Londonderry, UK

In previous responses to this question, the large deviations from 45 degrees for the optimum launch angle for maximum range of a garden hose were wrongly attributed to the effect of air resistance (3 September).

Such deviations are predicted, without air resistance, when projectiles are launched from a height above ground level. If the hose is at shoulder height (around 1.5 metres, say) and the initial water velocity is 1 metre per second, then, according to my calculations, the optimal angle should be 10.2 degrees, not 45 degrees. Effects of air resistance cause a less than 5 per cent reduction of these predicted optimum launch angles.

Chris Daniel
Colwyn Bay, Conwy, UK

The distance travelled by a stream of water from a hose depends on the flow rate, the angle of the nozzle and its height from the ground. When the hose is held well above ground level, the water will travel further when the hose is angled at less than 45 degrees, as the questioner observed.

Ignoring any air resistance, a jet of water from a hose will follow a parabolic curve. When the hose is held at ground level, water will travel the greatest horizontal distance when the nozzle is angled upwards at 45 degrees. As the arc of water rises from this starting point, its slope decreases from the initial angle – 45 degrees in this case – to zero as it reaches its peak then continues to decrease as it descends until it hits the ground at minus 45 degrees.

A gardener would normally hold the hose at some convenient height above the ground. This can be thought of as the hose being positioned further up and along the imaginary rising part of a parabola that starts with an angle of 45 degrees from ground level behind the gardener. The hose therefore has to be angled at less than 45 degrees to be aligned with the parabola’s decreasing slope at this position to ensure that the jet of water travels the furthest possible distance.

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