Sailboat Speed Question: Can a Motor Increase Speed Beyond 10 Knots with Sails?

[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?

 

[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.

 

[anorlunda]

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.

 

[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?

 

[Hercuflea]

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.

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.

 

[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?

 

[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.

 

[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.

 

[Hercuflea]

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.

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.

 

[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.

 

[jbriggs444]

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.

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.

 

[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.

 

[A.T.]

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

How much increase compared to motor alone is the question.

 

[A.T.]

Your motor that can push a boat at 5 knots will actually be a drag on a boat that is doing 10 knots

That is not necessarily true.

 

[A.T.]

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.

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

 

[anorlunda]

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.

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 .

Fun thread.

 

[CWatters]

The short answer is that there is no short answer.

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.

 

[DaveC426913]

Your motor that can push a boat at 5 knots will actually be a drag on a boat that is doing 10 knots

That is not necessarily true.

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.

 

[DaveC426913]

The short answer is that there is no short answer.

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.

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)?

 

[jbriggs444]

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.

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.

 

[DaveC426913]

That is not necessarily true.

Hm. Actually I can think of a circumstance where I am wrong, though it is highly-contrived to make the point.

I can posit a configuration where (a motor that can only push a boat through the water at 5 knots) does not cause any drag when sailing at 10 knots.

Imagine a giant 200HP motor with a teeny 5 inch propellor.
The prop spins very fast due to powerful motor and its gearing - but because the actual prop is so small, it can only push the boat along at 5 knots.

Now, we fire up the sails and reach 10knots.
The prop is spinning very fast. So fast that it is not only not a drag, but it still provides a tiny additional thrust, no matter how fast the boat is sailing.

OK, so it is possible, in principle, to have a motor that can only move the boat at 5 knots, yet not provide any drag while sailing at 10 knots.

 

[DaveC426913]

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).

My objection here is that simply "making it spin faster" does not automatically equal thrust.

A freely-spinning prop produces drag.
A slowly-spinning prop still produces drag.
A prop that is engaged with an idling motor, and is therefore spinning too slow, will definitely produce drag.
You must power up the motor so that the prop is spinning fast enough in 10 knot water flow so as to produce zero drag.

The question then becomes: can a motor (that is only powerful enough to move the boat at 5 knots) spin the prop fast enough to reduce drag to zero and beyond, to thrust?

 

[jbriggs444]

The question then becomes: can a motor (that is only powerful enough to move the boat at 5 knots) spin the prop fast enough to reduce drag to zero and beyond, to thrust?

So the comparison you are attempting to make is between a retractable prop and a non-retractable prop powered by a 5-knot-capable motor.

 

[anorlunda]

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)?

Any motor of any non-trivial size with any nonzero efficiency can increase the sailboat speed some increment.

 

[DaveC426913]

Any motor of any non-trivial size with any nonzero efficiency can increase the sailboat speed some increment.

No. This is not true.

Lets look at it in increments.

1] We have a disengaged prop and the motor is off. Prop provides some drag (indeed, this is why feathering props were invented).
2] We start the motor in neutral. No change (prop continues to spin freely), still producing same drag.
3] We engage the drive train (throw it into gear). Prop stops completely. Maximum drag. We do not get to take advantage of the boat's movement spinning the prop.
4] We throttle up. Prop spins faster, drag is reduced but not yet eliminated. Prop will not move any faster than drive train will allow.
5] Iff we can throttle the prop up to a high enough speed, where it is producing zero drag in a 10 knot current - then we now have a motor that can push the boat past 10 knots.

 

[A.T.]

Lets look at it in increments.

How about looking at the actual physics? Any amount of mechanical power an engine can deliver can be turned into forward thrust at any speed, given the right gearing / pitch and sufficient efficiency:

F = eta * P / V

 

[CWatters]

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)?

Clearly it could subject to some design details.

However the OP asked if it could get to 15 knots. If the motor power is what limits it to 5 knots without a sail then you need to find a way around the fact that drag is proportional to velocity cubed. Otherwise the motor won't add enough power to get to 15 knots.

Rigging a 200 HP motor so it only does 5 knots is a bit of a cheat. Although the Schneider Trophy sea planes of the 1930's had a similar problem. They were capable of very high speeds (for their time), yet had a problem taking off because their fixed pitch propeller was optimised for high speed flight not low speed acceleration over water.

 

[cjl]

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)?

This will depend on the propwash speed. I don't know what the normal slip ratio of a boat propeller is, but if, while moving at 5 knots, the prop is pushing water backwards at 15 knots (relative to the boat), then it should still provide positive thrust at that rotational speed all the way up to a boat speed of 15 knots. In addition, as the boat goes faster, the load on the prop will decrease (at a given RPM), as the inflow speed increases. As such, I'd expect the prop RPM to climb somewhat, further pushing out the point at which the prop could no longer help matters.

 

[gleem]

If the engine in the OP was designed to push the boat at five knots considering its displacement water line length propeller diameter and pitch and engine HP and max rpm. and was capable of 10 knots under sail. you are talking about a boat with about a 75 ft waterline length. Now since the prop was designed to operate at 5 knots the angle of attack of the water is optimal for some rpm probably about 75% of max. The prop to exert any thrust will have to turn at a much much higher rpm and the pitch would have to be dramatically increased.

The hydrodynamic drag varies about as the square of the speed. so to go from 10 to 15 knots one would need to exert a force of about 2.25 time greater. But the force to move the boat at 10 knots is 4 time that to move it at 5. so it seem you would need 4 x 2.25 =9 times more force or did I just embarrass myself. Now as the boat speeds up the drive from the sails can increase (apparent velocity increases) but this increase in drive cannot be free although I cannot see the connection between the increased sail power and the energy used by the motor.

 

[anorlunda]

No. This is not true.

Lets look at it in increments.

1] We have a disengaged prop and the motor is off. Prop provides some drag (indeed, this is why feathering props were invented).
2] We start the motor in neutral. No change (prop continues to spin freely), still producing same drag.
3] We engage the drive train (throw it into gear). Prop stops completely. Maximum drag. We do not get to take advantage of the boat's movement spinning the prop.
4] We throttle up. Prop spins faster, drag is reduced but not yet eliminated. Prop will not move any faster than drive train will allow.
5] Iff we can throttle the prop up to a high enough speed, where it is producing zero drag in a 10 knot current - then we now have a motor that can push the boat past 10 knots.

I like this thread.

Everything you said is correct. But you are equating RPM with power.

My sailboat is 29 feet long at the waterline, weighs 25000 pounds, and has a 30 hp engine. The fastest I have ever traveled under sail with zero current is 9 knots (way above hull speed, and in very strong wind conditions). At that speed, it takes about 5% power to spin the prop fast enough to eliminate its drag. That is about 1.5 hp, and in the range of what I meant to exclude by the word non-trivial in #24. Adding more than 5% power makes me go faster.

 

[A.T.]

I confess, I am not certain my logic is airtight,

I confess, I don't follow your logic at all:

- The maximal speed achievable by pure motor depends, among other things, on the drag parameters of the boat
- The maximal speed at which a certain motor/gearing/pitch combo can still produce forward thrust is completely independent of those drag parameters of the boat.

So I don't see any reason to assume these speeds to be equal.

 

[Hercuflea]

Currently on a long drive to Arkansas, but I'll try to respond with a mathematical model later for criticism.

 

[DaveC426913]

OK, I'm a layperson who is in over my head. I'm cryin' uncle.

 

[DaveC426913]

My sailboat is 29 feet long at the waterline, weighs 25000 pounds, and has a 30 hp engine.

Huh. My sailboat is 4/5ths as long, and 1/10th as heavy (yes, one-tenth), yet has 2/3rds more power.
(And a semi-planing hull)

(That sounded like bragging. It wasn't mean to be. I was merely astonished at the range of configurations of boats.)

The fastest I have ever traveled under sail with zero current is 9 knots (way above hull speed, and in very strong wind conditions).

You were surfing down a wave I presume. (Well, I guess you'd pretty much have to be. Since you were well beyond hull speed, you were riding down your own bow wave)

I don't count any of my record sail speeds that are not sustained for at least 15 seconds. 6.7 is my top sustained.
(14.0 is my top, under power)

 

[anorlunda]

Huh. My sailboat is 4/5ths as long, and 1/10th as heavy (yes, one-tenth), yet has 2/3rds more power.
(And a semi-planing hull)

(That sounded like bragging. It wasn't mean to be. I was merely astonished at the range of configurations of boats.)You were surfing down a wave I presume. (Well, I guess you'd pretty much have to be. Since you were well beyond hull speed, you were riding down your own bow wave)

I don't count any of my record sail speeds that are not sustained for at least 15 seconds. 6.7 is my top sustained.
(14.0 is my top, under power)

Yes the variations are huge. That is why displacement is a better measure of size than length. Mine, a Westsail 32, is famous as perhaps the toughest cruising boat ever built. The W32 Satori, survived The Perfect Storm without damage.

Your specs sound like a MacGregor 26; the opposite design extreme than the Westsail.

Hull speed is where you start climbing your own bow wave. The speed where you reach the top of that wave is much higher. So you can exceed hull speed without surfing or planing. When I did 9 knots it was sustained. I know that I could not have been at the top of my bow wave because I still had pitch stability. I averaged 7.5 over 24 hours that day, but my hull speed is 7.2 (By the way I had a feathering prop, so no prop drag of the kind discussed in this thread.)

I guess you can tell I like talking about boats.