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.

 

[DaveC426913]

Your specs sound like a MacGregor 26;

I guess you can tell I like talking about boats.

And I like the cut of your jib!(Ah, you're from Florida. No wonder you recognize a Mac. It's on their migratory route.)

 

[Atfirst]

Interesting question. The answer is a plain NO however, no way you are ever going to reach 15 knots ! I own a 31 foot sailboat, that weighs 3.2 tons and has an inboard diesel of 18 hp. In flat water with no sails up I make about 5.5 knots with the engine running at about 2000 rpm. Under sail only, sailing close hauled in a 15 knot wind I make about the same speed. When motor-sailing in the same condition, that is sailing at 5.5 knots and having the engine running at 2000 rpm I will certainly go faster but hardly more than 1 knot. So the propeller most definitely does not cause a drag under these conditions. During maintenance of the engine (and being securely tied to the pontoon) I sometimes run the enigine at full throttle. I have never measured the speed of the water that is being ejected from the back of the boat but it is by all means in excess of 10 knots and probably substantially more. I conclude therefore that if I could sail at e.g. 7 knot and then start the engine at full throttle I would still experience a forward thrust from the propeller but I suspect I wouldn't gain much more than half a knot, if that much.

 

[DaveC426913]

Interesting question. The answer is a plain NO however, no way you are ever going to reach 15 knots ! I own a 31 foot sailboat, that weighs 3.2 tons and has an inboard diesel of 18 hp. In flat water with no sails up I make about 5.5 knots with the engine running at about 2000 rpm. Under sail only, sailing close hauled in a 15 knot wind I make about the same speed. When motor-sailing in the same condition, that is sailing at 5.5 knots and having the engine running at 2000 rpm I will certainly go faster but hardly more than 1 knot. So the propeller most definitely does not cause a drag under these conditions. During maintenance of the engine (and being securely tied to the pontoon) I sometimes run the enigine at full throttle. I have never measured the speed of the water that is being ejected from the back of the boat but it is by all means in excess of 10 knots and probably substantially more. I conclude therefore that if I could sail at e.g. 7 knot and then start the engine at full throttle I would still experience a forward thrust from the propeller but I suspect I wouldn't gain much more than half a knot, if that much.

Couple of things:

1] The numbers in the OP are arbitrary. All of us sailors know that 10 knots under sail is unrealistic. Doesn't affect the question.

2] Your particular sailboat is not designed to go fast under power. Some saiboats are designed to exceed 20 knots under power. Indeed, people can, and do, use them for waterskiing.

 

[Hercuflea]

I hope everyone who responded to this thread is still around!
I have no experience sailing, but let me try to model the physics of the situation.
Suppose the boat is traveling on calm water with a speed $v₀=10$ knots in the positive $x$ direction.
Now drop a small motor into the water and turn it on at full power (the motor can propel the boat in the same conditions at 5 knots under it's own power).
Assumptions:
The wind speed is constant, the boat is traveling at the optimal angle of attack to maximize its speed, and its maximum speed under sail only in these conditions is $v₀$.

The factors that go into determining the boat's speed at this point are:
$F_{s}=$ the force exerted by the sails on the boat at the given wind speed $v_{w}$. (Newtons)
$P_{m}=$ the power output of the motor (kW)
$D=$ the drag force exerted by the water on the hull of the boat, opposite the direction of travel. (N)
$D_{m}=$ the drag force exerted on the motor in the same direction as $D_{h}$ after the motor has been dropped. (N)
$v_{b}(t)=$the velocity of the boat at time t. (m/s)
$v_{a}=v_{b}-v_{w}=$ the apparent wind speed. This is what determines the value of $F_{s}$, not the true wind speed. (m/s)

Now, the motor and the sails have to have a common parameter that we can compare them with. I think the most common way we would describe a sail is the amount of force it exerts on the boat, but the most common way we would describe a motor is the amount of power it outputs. I am not sure how to convert propeller power to force in the forward direction, but I do know from elementary mechanics that

$Power=Force⋅velocity$

So, we can convert the force variables to power variables so that everything has the same dimensions (and are scalars instead of vectors).

$P_{s} = F_{s}⋅v_{b}$,power of the sails (kW)
$P_{m} = P_{m}$ (measurable power of motor, kW)
$P_{d} = (D+D_{m})⋅v_{b}$,power expended by drag forces, kW


The sail-force $F_{s}$ must be some function of the apparent wind velocity $v_{a}=v_{b}-v_{w}$. I'm not sure how to convert incoming wind velocity into force.
The boat's velocity $v_{b}$ is a function of:
The propeller power
The sail force (and thus sail power) (negative sign)
The drag force (and thus drag power) (negative sign)
boat mass $m$
acceleration $a$
Setting the total boat power equal to the sum of the powers:

$$P = P_{s}+P_{m}+P_{d}$$
⇒
$$(∑_{i}F_{i})⋅v_{b} = F_{s}⋅v_{b}+P_{m}+(D+D_{m})⋅v_{b}$$
$$(ma)⋅v_{b} = P_{m}+(F_{s}+D+D_{m})⋅v_{b}$$
$$v_{b}⋅((∂v_{b})/(∂t)) = ((P_{m})/m)+(1/m)(F_{s}+D+D_{m})⋅v_{b}
$$

Is there an easier way to do this? You could just look at the sum of forces itself, but then you need a way to convert motor power in kW to Force in N? Seems like there's an extra unknown somewhere.

(vectors need to have arrow signs but I'm not sure how to add those)

 

[gleem]

I posted an approach in post #29.

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.

This can be further extend to the power need.

Speed 5kts 10knt
Net
Force(rel units) 1 4

HP (rel units) 5 40

So how much more speed does 25 hp units buy you if you are already going 10 kts.?

I propose adding 25 to the 160 and determine the speed assuming there is no change in the force speed relationship.

You get 10.4 kts.

YUCK! I would hope that real sailors would not consider this a true sailboat...I think it has a 60 Hp motor hanging off its stern. It is probably a terrible sailing boat. The weight of the engine alone would probably mess up its performance.

Note added: The propeller must be changed from that used at 5 kts since its pitch will be inappropriate for significantly higher speed. You must Increase the pitch.

 

[rcgldr]

To reiterate what I posted earlier, the flow relative to the propeller is different than the boat's speed relative to the water because the propeller operates in the wake of the boat. From Wiki: "Wake is the interaction between the ship and the water with its own velocity relative to the ship. The wake has three parts: the velocity of the water around the hull; the boundary layer between the water dragged by the hull and the surrounding flow; and the waves created by the movement of the ship. The first two parts will reduce the velocity of water into the propeller, the third will either increase or decrease the velocity depending on whether the waves create a crest or trough at the propeller."

http://en.wikipedia.org/wiki/Propeller#Actual_performance

The unknown here is the difference between boat speed relative to water and wake speed relative to propeller.

 

[gleem]

To reiterate what I posted earlier, the flow relative to the propeller is different than the boat's speed relative to the water because the propeller operates in the wake of the boat. From Wiki: "Wake is the interaction between the ship and the water with its own velocity relative to the ship. The wake has three parts: the velocity of the water around the hull; the boundary layer between the water dragged by the hull and the surrounding flow; and the waves created by the movement of the ship. The first two parts will reduce the velocity of water into the propeller, the third will either increase or decrease the velocity depending on whether the waves create a crest or trough at the propeller."

This might be true for an outboard but many sailboats have inboard power with the prop mounted well below the water surface in the non turbulent laminar flow of water aft of the keel and typically two to 10 feet behind the transom and the wake.depending on the size of the boat. So your problem need not be generally addressed.

 

[DaveC426913]

YUCK! I would hope that real sailors would not consider this a true sailboat...

Ah. The ol' No True Scotsman fallacy.

Yup. Well aware of the jealosy that motorsailers engender.

A sailor is someone who sails a boat (unless you're in the Navy or a Church St. bar on Toronto). And there are as many types of sailor as there are sailboats.
Sailboats come in a vast array of configurations to meet every sailor's preferences.
By definition, those who buy a given sailboat, do so because its merits beat those of every other sailboat.

 

[DaveC426913]

... many sailboats have inboard power with the prop mounted well below the water surface in the non turbulent laminar flow of water aft of the keel and typically two to 10 feet behind the transom and the wake...

Sorry, did I read that right?

What I read is you stating that typically, inboards have the prop 2 to 10 feet behind the transom (never mind the wake).

C̶a̶n̶ ̶y̶o̶u̶ ̶s̶h̶o̶w̶ ̶m̶e̶ ̶a̶ ̶s̶i̶n̶g̶l̶e̶ ̶e̶x̶a̶m̶p̶l̶e̶ ̶o̶f̶ ̶a̶ ̶m̶o̶d̶e̶r̶n̶ ̶s̶a̶i̶l̶b̶o̶a̶t̶ ̶w̶i̶t̶h̶ ̶i̶n̶b̶o̶a̶r̶d̶ ̶t̶h̶a̶t̶ ̶h̶a̶s̶ ̶i̶t̶s̶ ̶p̶r̶o̶p̶ ̶a̶f̶t̶ ̶o̶f̶ ̶t̶h̶e̶ ̶t̶r̶a̶n̶s̶o̶m̶ ̶b̶y̶ ̶a̶n̶y̶ ̶a̶m̶o̶u̶n̶t̶,̶ ̶l̶e̶t̶ ̶a̶l̶o̶n̶e̶ ̶2̶ ̶-̶1̶0̶ ̶f̶e̶e̶t̶?̶

No ... you're saying the laminar flow is 2-10 feet behind the keel.
But how does that address whether the prop is in an area of laminar flow?

 

[gleem]

OOps but really you know what I meant, behind looking forward?? Should have said forward of the stern. By the way I am sorry if that was your boat. But that isn't even a proper motor sailer. IMHO.

 

[DaveC426913]

By the way I am sorry if that was your boat. But that isn't even a proper motor sailer. IMHO.

It is my boat. I frequently bask in the glow of jealous sailors, who seem to think their idea of sailing is the only one there is.

Tell you what? Let's go out together one day, and have some fun:

1. We'll sail in ridiculously high winds that knock us over to 45 degrees even when reefed. I'll have helm because my twin keels will still be in the water. What's your max heel before you lose helm?
2. We'll wait until a squall is right on top of us before deciding it's time to head for shelter. I'm there in five minutes. You?
3. Then, when we get bored of this lake by lunch, we'll haul our boats out, and trailer them (behind our 6-cylinder sedan) to another lake for the afternoon.
4. We'll head up a nice cozy river, under a few bridges. I need 11 feet of overhead clearance. You?
5. We'll go right up to the head of the river. My draft is 12 inches. Yours?
6. At sunset, we'll pull right up and beach on the shore of a sandy lagoon and play in the surf.
7. When the wind dies to zero, I'll tow you back to harbour in a half hour.

 

[gleem]

I am glad you are happy with your choice and maybe some astute business man found a niche or larger. but I still say a pox on it. Beauty is in the eye of the beholder and I see none.. I do not see a lot of competition in that market for that concept. I might add that this idea is not new. Back in the early 80's there was an identical idea although I forget the manufacturer, out of business.

So when are you going to the Caribbean ?

 

[gleem]

@DaveC426913 I want to apologize for my elitist/snobbish comments. I have not sailed the boat so I should not have made those comments. It obviously suits your needs and I appreciate its flexibility and advantages. Now back to the OP.

 

[DaveC426913]

No worries at all!

You wouldn't be a sailor if you didn't have strong feelings about boats. It's a requirement!

 

[Hercuflea]

So has this thread come to any consensus at all about the op?