# B Sailboat speed question

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1. Nov 3, 2016

### Hercuflea

This is not a homework question, I'm just curious.

Suppose you had a sailboat sailing on calm water.

Let's say the sailboat is capable of sailing at 10 knots under the current wind conditions using only its sails.

Now say the sailboat had a small propeller motor that was capable of propelling the boat at 5 knots under its own power without help from the sails.

If the boat was at full sail, and you ran the motor at the same time, would the boat reach a speed of 15 knots? Would it stay at 10 knots since the motor could not propel the boat above 5?

Or would the speed actually decrease to below 10 knots due to the friction between the motor and the water?

2. Nov 3, 2016

### Cutter Ketch

Hmm... fun question. I don't think the answer always has to be one way or the other, but I believe in most cases the propeller will be a drag, not a thrust. A propeller is like a wing moving in circles. The blades have an angle. When no water is flowing along the axis of the propeller (zero boat speed) the blades cut through the water at their full angle of attack. As the axial speed of the water increases the effective angle of attack decreases. Propellers are designed to work over a range of angles of attack as determined by the rotation speed and the expected maximum axial flow. However eventually at high enough forward speed even turning as fast as the motor can spin the propeller the angle of attack starts to become shallow and the thrust falls off. At the same time, as the boat moves faster and faster the drag force increases. If a motor can only move a boat at 5 knots that doesn't mean the angle of attack has reached the point that the thrust is zero. It means that the thrust of the propeller is equal to the drag of the boat. It is possible that the angle of attack will still be positive and that a propeller will continue to make a small thrust at double that speed through the water, just not enough thrust to equal the drag of the boat moving that fast. However, I believe most of the time the top speed is at least partially due the propeller losing thrust as the angle of attack shallows, and so I believe most of the time at double the motor/propeller's top speed the angle of attack will become negative and the propeller will be a drag, not a thrust. However, that is just a speculation and physics easily allows the opposite case.

3. Nov 3, 2016

### Staff: Mentor

You didn't say which way the wind was blowing.
• It the wind is from behind the boat, then apparent wind speed is true wind speed minus boat speed. Turning on the motor makes the force on the sail less. Enough motor can make the wind force on the sail zero or negative.
• If the boat is heading into the wind (30 degrees is a close to the wind as it can get) then apparent wind is true wind plus boat speed. Turning on the motor increases apparent wind speed and makes the sail more efficient, allowing higher speeds and angles even closer to the wind.
You are also neglecting hull speed. That is a speed at which resistance of the water grows nonlinearly. It is not a brick wall to increase speed but it is very significant. Hill speed depends on the length of the boat, wind and or motor power don't matter.

Cruising sailors often motor sail.

4. Nov 3, 2016

### Hercuflea

Hmm. I have always wondered if it would be possible to build a hybrid solar sailboat and this always comes up. I guess you would need to have a solar powered motor powerful enough to provide thrust greater than or equal to the thrust of the sails?

5. Nov 3, 2016

### Hercuflea

Just saw your post. (I've always assumed the wind is pushing the sail forward)

I didn't think about that. So the sail thrust is actually a decreasing function of the motor thrust. As the motor thrust increases, the boat speed increases which decreases the wind speed hitting the sail. So if the motor was more powerful than the sail, the sail would just be a drag on the motor.

6. Nov 3, 2016

### rcgldr

I'm wondering what the effects of the hull dragging the water along. What if the propeller is operating within the wake produced by the hull?

7. Nov 3, 2016

### Cutter Ketch

To anorlunda ... I really don't think any of that is relevant. The boat is sailing along at 10 knots on any point of sail you care to mention. Drop the motor and fire it up. If the boat accelerates the motor added thrust. If the boat decelerates the motor was a drag. The question is already answered. In all cases except the case where the motor is neutral the sails will become less efficient (assuming they were optimized for the initial condition) and will have to be retrimmed. That is only an issue after the motor has changed the speed of the boat and the question has been answered. Regarding hull speed, the question only asked for the sign of the motor's contribution not the magnitude. Regarding motor sailing, that is always in conditions where the sails aren't moving the boat as fast as the motor.

8. Nov 3, 2016

### jbriggs444

One should examine the mechanism of the motor, propeller and gearing. A motor that has sufficient power to move a boat at 5 knots has grossly inadequate power to increase the speed of a boat moving at 10 knots by another 5 knots

This is much the same way that a motor that has sufficient power to move a car at 50 miles per hour has grossly inadequate power to increase the speed of that same car from 100 miles per hour to 150 miles per hour.

9. Nov 3, 2016

### Hercuflea

So would that imply that adding a solar powered motor to a sailboat would be self-defeating? If the motor thrust is less than the sail thrust, then the motor is a drag on the sail. If the motor thrust is greater than the sail thrust, the sail is a drag on the motor. If the two thrusts equal, I imagine they do not add together.

10. Nov 3, 2016

### sandy stone

In my experience, starting the motor on my sailboat and putting it in gear *always* increases boat speed. Let the theorists explain experimental results.

11. Nov 3, 2016

### jbriggs444

No, that's not it at all. As long as you gear the motor up so that the prop spins fast enough (albeit with reduced force), you can gain some advantage. Just nowhere near 5 knots worth.

12. Nov 3, 2016

### DaveC426913

Couple of things:

1] Motor-sailing is a common technique (did it just last weekend for about 10 miles). As long as the sail has wind in it, it is providing forward movement . You can run your motor at a speed from 0 all the way up to 10 knots. You'll save gas and also keep a good constant speed. But the boat (which, at 10 knots, now has flogging sails) won't exceed 10 knots - unless the motor can exceed 10 knots.

2] Your motor that can push a boat at 5 knots will actually be a drag on a boat that is doing 10 knots - the water is moving past the motor at 10 knots. The motor would have to be working at no less than 10 knots to provide any advantage.

13. Nov 4, 2016

### A.T.

How much increase compared to motor alone is the question.

14. Nov 4, 2016

### A.T.

That is not necessarily true.

15. Nov 4, 2016

### A.T.

Note that this assumes optimal gearing / propeller pitch so the motor actually delivers the same power in both cases.

16. Nov 4, 2016

### Staff: Mentor

No, the implication is false. In fact there are a lot of false answers on this thread.

I motor sail often. The usual reason is to maintain a minimum speed to guarantee arrival at port by some deadline. It is most efficient with the motor at near idle speed. For escape, in light winds I can still only at 3 knots with a 6 knot winds from behind.. Running the motor at idle (800 RPM) brings it to 4 knots. 1200 RPM gets me 4.5 knots. (That is a 50% gain in speed using very little fuel. That would be ideal for a solar hybrid.) To go faster than 4.5 in that wind, I would have to take the sails down and ramp up motor power. 100% motor power, @2100 RPM, makes me go 6 knots.

To visualize propeller thrust, compare it to a jet engine, or a rocket. Forward thrust comes from propelling a small mass backward at high speed. To push a boat at 5 knots, the propeller pushes a small amount of water back at say 20 knots. If the boat was moving at 10 knots, there is still some forward thrust. Even at 20 knots, there is still forward thrust. I don't know how to calculate the speed where thrust is zero, but it would be pretty high. Ditto for a propeller driven airplane ; the zero thrust speed will be much higher than the plane's max speed.

The power needed to push a boat through water is highly nonlinear. Consider a non- planning hull with a hull speed of 7 knots. It may need 1 unit of power to go 2 knots, 3 units to go 4 knots, 10 units to go 6 knots, and 40 units to go 8 knots. That is the flaw in the OP question. It may be impossible to make that boat go 15 knots given all reasonable wind plus motor power. But if the OP asked about changing speed 50% from 1 knot to 1.5 knots, the answer would be very different. At that low speed, a sneeze might be enough to go faster .

17. Nov 4, 2016

### CWatters

A lot depends on design parameters. Even F1 cars occasionally get it wrong. Towards the end of a long straight they sometimes find they have the power but not the right gearing to go faster.

In general the power required to overcome drag (air of water) isn't linear so it takes a lot more power to increase speed from 10 to 15 knots than it does to go from 0 to 5 knots even though both are a 5 knot increase. If your motor is developing max power at 5knots then it's very unlikely to be able to increase the speed from 10 to 15 knots when under sail. But that's not to say turning the motor on can never increase the speed when under sail.

18. Nov 4, 2016

### DaveC426913

I confess, I am not certain my logic is airtight, but under what circumstances might it not be true?

Let's first pretend that, rather than rigidly cranking too slow for 10 knots, the prop is disengaged and allowed to spin freely. It still provides a small amount of drag.

In order to create no drag, the prop would have to be spinning so fast as to either provide zero drag or provide thrust - while moving at 10 knots.

19. Nov 4, 2016

### DaveC426913

While this is all true, I think there is still value in examining the question in principle - eg. assume there is no gearing issue, etc.

Can
a motor (that can push a boat at 5 knots), increase the top speed of a boat under sail at 10 knots (when the motor is operating optimally)?

20. Nov 4, 2016

### jbriggs444

It takes zero power to allow the prop to spin. With appropriate gearing, any added power could make it spin faster and generate some thrust (or at least reduce the drag from the otherwise free-spinning, non-retractable prop).

Mind you, I am not suggesting that real world motor sailers contain a variable speed gearbox that would allow such or that their prop shapes are designed to suit such manipulations.