## Speed, Range and Power Relationships for Electric Sailing…

# Speed, Range and Power Relationships for Electric Sailing…

In a recent discussion with someone considering an electric drive system for his sailboat, I was explaining some of the relationships between speed, power, and range. The amount of power needed to push the boat at a given speed has a cubic, or third order, relationship (at the speeds we’re talking about for sailing).

I’ll recap a few points about these relationships in this article.

There are a few equations that let us calculate “hull speed” (or maximum speed for a non-planing boat hull), and the power needed at the propeller to maintain a given speed. Below is an example graph for a 26.5′ Beneteau.

Example Speed Power Relationship Graph

When considering what size battery to put into your electric-drive sailboat, it helps to understand this relationship. Of course, a main take-away here is that you can motor for a very long time if you don’t start climbing the steep part of this curve. When you go relatively slowly, the energy stored in your battery will take you much further than when you start approaching your boats hull-speed.

For this small Beneteau, long motoring trips above 4.6 knots starts to take a significant amount of power.

The Beneteau First 26.5, has a length at the waterline of 24.2-foot, so the hull speed is about 6.6 knots.

This comes from the equation:

HULLSPEED = 1.34*SQRT(LWL)

where LWL is the length at the waterline

If we establish a recommended cruising speed at 70% of the hull speed we get 4.6 knots as the cruising speed for this boat.

With this, we can estimate the power needed to move at 4.6 knots to be about 960 watts (or just under 1 kW).

Using 1kW as our power estimate, with a 10 kWh LFP battery, we can estimate a cruising time to be about 8.0 hours.

This is because, we don’t want to deplete the battery to 0% charge, and we’ll want some power available for getting in and out of the marina(s). Let’s estimate we will always keep a minimum of 10% charge in the battery and that we’ll use 10% of the charge for motoring around while not cruising to a destination. This leaves us with 8 hours of motoring, at a speed of 4.6 knots.

In my experience, motoring slower is well worth it, if the winds are light or not present at all. Using only 500 watts (half the power) will still move this boat at about 4 knots, and for a much much longer time.

Hopefully, this example helps clarify how an electric propulsion system’s battery can be used most effectively on a sailboat. Range from the motor extends dramatically at lower speeds. Travel at Hull-Speed, when the wind is blowing strong.