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Last Word is Â鶹´«Ã½â€™s long-running series in which readers give scientific answers to each other’s questions, ranging from the minutiae of everyday life to absurd astronomical hypotheticals. To answer a question or ask a new one, email lastword@newscientist.com

When driving over hills, which is more fuel-efficient: accelerating downhill for uphill momentum or maintaining a steady speed?

Eric Kvaalen
Les Essarts-le-Roi, France

It is more fuel-efficient to maintain a steady speed because the total energy used depends on the average air resistance. Since air resistance is proportional to the square of speed, your average resistance will be lower at a steady speed, compared with going fast and then slow at the same average speed.

However, there are other considerations. When going downhill, you can save fuel by pushing the clutch so that the engine turns at idle. And if you are going over the top of a hill, allow gravity to slow down and speed up your vehicle, rather than using fuel to keep your speed constant all the way to the top.

For example, there is a bridge over a railway near where I live. Here, I let gravity slow the car down as I approach the top, then let it speed me up again going back down. This is a bit slower overall, but it saves fuel.

Chris Daniel
Glan Conwy, UK

It is more efficient to let a car with an internal combustion engine on an undulating road accelerate using gravity on downhill sections to convert the potential energy to kinetic energy. This can then be used on the following uphill stretch, allowing for losses due to wind resistance and friction in the wheels and engine.

Adopting this method will reduce the fuel consumption for the journey compared with using the brakes or low-gearing to maintain a steady speed, which causes the excess kinetic energy to be lost in the form of heat.

A different strategy can be used in electric vehicles. Many now have energy-recovery systems in the form of regenerative braking, which is reportedly 60 to 70 per cent efficient, and kinetic-energy recovery, which operates when the foot is taken off the accelerator and can be up to 85 per cent efficient. This means that instead of freewheeling down a slope under gravitational acceleration, a steady speed can be maintained and much of the excess kinetic energy converted to chemical potential energy in the batteries, to be used later. This technology offers a more flexible way of driving.

Hillary Shaw
Newport, Shropshire, UK

In driving lessons, I was told, “Go down a hill the same speed you would go up it” and use “more fuel for the hill (upwards)”. Cars use large amounts of fuel just to overcome air resistance, which increases at higher speeds. If you stick to 70 kilometres per hour on a motorway rather than doing up to 80 km/h, you see the fuel economy gain, about 15 per cent in my car. So a steady speed is best.

Ian Smith
Chipping Norton, Oxfordshire, UK

Maintaining a steady speed is more energy-efficient, as aerodynamic drag increases (roughly) as the square of velocity. Basically, the faster you are going at the bottom of the hill, the more energy is going to be lost through drag. This rapid increase in drag with velocity is quite apparent to those (like me) who drive electric vehicles. The kilometres per kilowatt-hour figure drops quite noticeably if I increase my speed on a long trip from 90 km/h to 100 km/h, along with the predicted range, both of which are displayed prominently on the dashboard.

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