How do I find out the force on a mast?

[Bookmaker]

Hello.

I need to calculate the approximate rotational force on a mast and have no idea what formula I should use.

Based on a mast height and boom length giving me an amount of sail square footage, and a given amount of wind in knots, how much (in foot pounds) of force will be applied to the mast trying to 'rotate' it around. So I'm looking for some kind of formula. Any help out there? Thank you in advance.

[MikeJohns]

Not entirely sure what you want to calculate, but the heeling moment from the rig is in equilibrium with the righting moment from the hull, usually taken at 30 degrees heel.

If it's stayed then the mast is in compression and the stays are in tension. If not stayed then its the standard beam with bending moment and shear.

You might want to read "Principles of Yacht design" or something similar for a primer.

If you actually want to calculate torsional forces, they are the least of your worries, if the mast doesn't buckle it will be torsionally stiff enough.

[haru]

Please provide a picture explaining the setup. Also provide any info, and then elaborate your question as detailed as possible.
This may seem exaggerated but in this kind of setup one different info can mean lots of work. Actually, for each connection point a formula need to be created plus some more work depending on your questions.

[Paul Kotzebue]

Hello.

I need to calculate the approximate rotational force on a mast and have no idea what formula I should use.

Based on a mast height and boom length giving me an amount of sail square footage, and a given amount of wind in knots, how much (in foot pounds) of force will be applied to the mast trying to 'rotate' it around. So I'm looking for some kind of formula. Any help out there? Thank you in advance.

I'm assuming you mean the mast rotating about a vertical axis.

If the mainsail and boom are free to rotate about the axis of the mainsail luff (which most are), there will be no rotational force on the mast. It's a hinged connection that has no moments.

[gonzo]

There is going to be a negligible force from the slides or boltrope.

[Paul Kotzebue]

Good point Gonzo. It is the relatively small rotational force at the boltrope that allows a freely rotating mast to rotate.

[gonzo]

It is too small to worry about. I don't think anyone calculates masts taking that into consideration.

[messabout]

Rotation,if any, depends on the positition of the shroud attachments. If the tangs are set rearward on the mast, then rotation moment is largely opposed. Whereas, if tangs are attached to the front of the mast, then rotation force is likely. In addition, the location of the gooseneck pin with respect to the mast center line is quite influential.

I suspect that the calculation of rotational moment could become very involved. Sail area, sheeting force, trim angle, even the L/D ratio of the sail, along with the hardware positioning variables.

[haru]

To simplify:

The sail calculations only need wind force and lift force on it.

At the boom base there is always a torque force down due to weight. When turning centrifugal force is added. With wind an additional torque force is added radially.

These same forces are transmitted to the connection point of the mast.

Then there are torque forces with or with out wind along the sail edges or stays. This is also transmitted to the mast at the connection point.

Then again there are torque forces along the inner sail edge and where it's connected.

Then there is the wind resistance force on the mast itself.

Add all up and you got the forces acting at the base of the mast.

That's about it. Note these do not include forces introduce by a boat or waves etc.

[Bookmaker]

OK. Though I appreciate all the things everyone has talked about when it comes to booms and pins and goosenecks, etc. this isn't what I need. Imagine that the boom was hard mounted to the mast and cannot rotate separate from the mast. Now, I want to rotate the entire mast and boom as one object. I need to calculate the amount of pressure in foot pounds that will attempt to rotate the mast. The formula would need to have a variable for the length of the boom, height of the mast and force of the wind and it would output an approximate amount of force in foot pounds that was trying to make that rotating mast... rotate. Any ideas?

[SamSam]

OK. Though I appreciate all the things everyone has talked about when it comes to booms and pins and goosenecks, etc. this isn't what I need. Imagine that the boom was hard mounted to the mast and cannot rotate separate from the mast. Now, I want to rotate the entire mast and boom as one object. I need to calculate the amount of pressure in foot pounds that will attempt to rotate the mast. The formula would need to have a variable for the length of the boom, height of the mast and force of the wind and it would output an approximate amount of force in foot pounds that was trying to make that rotating mast... rotate. Any ideas?
I would guess If the boom was mounted to the mast as one object there wouldn't be any rotational force as long as the main sheet was doing it's job and holding the tail of the boom in place.

On thinking about it more, the boom wouldn't exert any rotational force but the sail in it's track would. It wouldn't have leverage like a solidly mounted boom without the main sheets, that is x amount of force applied to a lever several feet long, but x amount of force applied to a lever the length of the distance from the track to the center of the mast, a lever a few inches long. But then again, the boom would resist any rotation from the sail on the track.

I know it doesn't answer your question on how to find the amount of force, but is just my guess on how the force might be applied. Does it make any sense?

[Bookmaker]

OK, I'll try again... Take away the sheet and let the wind move the mast freely. I still need to calculate this force.

[Bookmaker]

I understand that what I'm asking isn't normal for a typical rig. But go with me. If the full force of the wind on the sail was attempting to rotate the mast with nothing else to help, how much rotational force is applied to the mast?

[SamSam]

Sorry, I understand what you are asking but I'm no good with numbers and formulas.

[Grant Nelson]

what you want is simply the wind pressure on the sail... you can assume its located at the geometric center of the sail which will take into account all the variables you mention, and that will give you the arm - the distance to the mast, which which will give you your pounds per foot, or what ever related measure you need.

Someone else is going to have to tell you how to find that presure per sq foot (probably a search in the forum will find it)

But I wonder why you want this? Are you going to try to rotate the mast via some gears or something at the base of the mast? If you are going to use the traditional main sheet, then the rotational force is not that important, but rather the vertical righting arm and the stresses it puts on your mast (downward) and rig (pull upward)...

[Bookmaker]

As a purely theoretical exorcise I was looking at what it would take to put a powered motor on a mast to rotate the mast and boom rather than a sheet on a moving boom. Now, I know any powered system has all kinds of issues with reliability vs. a standard rig. But I still wanted to figure out what size powered motor would be needed to handle the forces that a strong force wind would apply to the motor at the base of the mast. I've found motors for rotating large antenna arrays that have a ft. lb. rating for wind resistance. So now I'm trying to find out what kind of pressures would be applied to this motor if it was attached to a mast, fixed boom and sail.

So I was looking for a formula that would tell me the ft. lbs of rotation pressure for a given mast height and boom length and a known wind in knots.

Now, I know there are all kinds of issues involved, but before I even look at those I just wanted to see if any of these motors are even in the ball park.

Of course, the other question is... has anyone ever see a powered rotating mast on a sailing yacht?

[TeddyDiver]

Anything with proper gearing.. It actually boils down how fast (or slow) you are willing to turn the mast and sail..

[messabout]

Are you thinking of a sheetless rig where the boom is rigidly attached to the mast? The motor would then rotate the mast to affect sail trim. If that is the case then torque requirements might vary all over the lot. You will have introduced variables beyond sail area, aspect ratio, and wind velocity.

You may be thinking of some variation of the so called "swing rig". If the rig has a jib as most of them do, then there is a whole other set of variables with which you must contend. To clarify "swing rig" it goes like this....... The boom is rigidly attached to the mast but is free to pivot in the vertical plane. The boom extends forward of the mast for some distance. The jib luff wire is attached to the forward end of the boom and the jib is sheeted to the boom extension near the mast. That is a crafty way to avoid vangs because the jib luff wire tends to depress the clew end of the main. The whole thing revolves about the mast center line and the jib relieves some of the strain on the mainsheet by partially counterbalancing the main. Not only that but the jib and the main are always in the same spacial relationship with one another. There are other factors that would seem to constitute some sort of advantage, like when on a dead run you need not pole the jib, etc.

This a rig that a lot of RC modelers have tinkered with. It works. In no case have I seen of one of these rigs that is sheetless but I confess to having tossed the idea around in my sick mind. Some of the RC modelers claim that downwind behavior is erratic but I have not experienced that problem with models. There are some other references to this kind of rig on the forum.

[LP]

Sounds like you are tending towards a wing mast. Messabouts ideas are balancing aero forces about the mast, which makes a lot of sense as there could be some extremely high rotational forces to be contended with. In wing theory, center of lift is approximately 25% cord. Devising a system where your center of lift is located at the mast centerline would reduce control forces tremendously.

Otherwise, rotational force is roughly moment arm times force. A crude estimate will place center of effort 1/3 of the distance aft of the luff (triangular rig). With a 15' boom, C/E would give you a 5 ft moment arm. If your sail is producing 100 lbs. of lift then you've got 500 ft.lbs. torque on the mast. If your sail is producing 1000 lbs. (?) of lift, then you've got 5000 ft.lbs. of torque on the mast. These should "ballpark" you if you are brainstorming something. Basic physics. Actual dynamic forces could cause things to vary.

Good Luck.

[Bookmaker]

LP, thank you so much for your reply. It's very close to giving me the ball park number I'm looking for, but maybe you could help me a little more if I gave you some dimensions. What if the mast sail area was 20 meters (or 65') in height and the boom 6 meters (or 20') in length, and the wind was coming at 50 knots? How would this calculate (in the roughest of measurements is fine) into ft.lbs of torque on the mast?

I'm looking at a chart of different rotators that have these Breaking Torques:
in/lbs 1) 29,163 2) 71,607 3) 102,072 4) 159,358 5) 428,773
Each of these is a different rotator, but they are getting larger and heavier.

And I'm trying to see if any of them can handle the torque of a sail that large in a stiff wind.
Thanks!

[SamSam]

LP, thank you so much for your reply. It's very close to giving me the ball park number I'm looking for, but maybe you could help me a little more if I gave you some dimensions. What if the mast sail area was 20 meters (or 65') in height and the boom 6 meters (or 20') in length, and the wind was coming at 50 knots? How would this calculate (in the roughest of measurements is fine) into ft.lbs of torque on the mast?

I'm looking at a chart of different rotators that have these Breaking Torques:
in/lbs 1) 29,163 2) 71,607 3) 102,072 4) 159,358 5) 428,773
Each of these is a different rotator, but they are getting larger and heavier.

And I'm trying to see if any of them can handle the torque of a sail that large in a stiff wind.
Thanks!I would think a bigger problem would be to design a mast that would withstand the torque.

[amolitor]

You can use the heeling moment of the boat to estimate the force on the sail. As indicated earlier, heeling moment at 30 degrees is pretty normal.

You know that, whatever the forces are on the sail, they are applying a moment that big to the boat. Solve for the force at the geometric center of the sail.

Now use the horizontal arm, as indicated earlier, to work out the moment applied to the mast.

The heeling moment of the boat is what matters most here. If your boat basically falls over in a breeze, the maximum force on the sail is going to be quite low. If your boat is immensely stable, then the wind can pick up quite a lot, and apply a great deal of force to the sail before the boat heels enough to spill much breeze and take the load off.

[LP]

From Skene's book on design, wind pressure is equal to .004*V^2(mph)*area(ft^2). Somebody jump in and tell me if I am completely misinterpreting theory here. Basic triangle: .5BH=.5*65*20=650ft^2.

50kts*1.15=57.5mph.

57.5^2=3306.

.004*3306=13.2lbs/ft^2

13.2*650ft^2=8595lbs.force.

8595*1/3=2865ft.lbs. torque

2865*12=34,380 in.lbs. torque

This could be a gross misinterpretation of design theory. Skene doesn't state whether this wind pressure is driving force(lift) created by the sails of if it is pressure created by any physical object as it stands in a wind stream. Personally, there are so many unknowns here, I'm hessitant to even present these numbers.

There are certainly other factor to contend with also. A big issue is how are you going to maintain sail shape. Close to the wind, your main sheet supplies a great amount of vanging force to flatten your sail.

Anyways, good luck and I hope you build a model first.

[haru]

To simplify we can say the center of the force is at the center of the sail.
Using the moment arm formula: t= r * F
In this case r=B/2 happens to be the middle of the boom.
32.5 ft * 8595lbs.force = 279337.5 ft lbs torque

[Petros]

use one pound wind pressure per square foot of sail area will give you a reasonable number. That would be high for most recreational sails, low for a wing sail.

Generally they consider force on the sail limited by the maximum righting moment the keel can generate, so that would limit maximum wind pressure on the sail. So you would need the hull design, keel wt, etc to determine actual loads.

[Bookmaker]

Thank you all for your information, I'm trying to get some rough numbers now.

[Bookmaker]

From Skene's book on design, wind pressure is equal to .004*V^2(mph)*area(ft^2). Somebody jump in and tell me if I am completely misinterpreting theory here. Basic triangle: .5BH=.5*65*20=650ft^2.

50kts*1.15=57.5mph.

57.5^2=3306.

.004*3306=13.2lbs/ft^2

13.2*650ft^2=8595lbs.force.

8595*1/3=2865ft.lbs. torque

2865*12=34,380 in.lbs. torque

This could be a gross misinterpretation of design theory. Skene doesn't state whether this wind pressure is driving force(lift) created by the sails of if it is pressure created by any physical object as it stands in a wind stream. Personally, there are so many unknowns here, I'm hessitant to even present these numbers.

There are certainly other factor to contend with also. A big issue is how are you going to maintain sail shape. Close to the wind, your main sheet supplies a great amount of vanging force to flatten your sail.

Anyways, good luck and I hope you build a model first.

LP,
I know these are grossly ball park numbers, but they do give me some hope since the rotator motor I was considering was 73,000 in/lb. rotating torque and 102,000 in/lb. braking torque. If the numbers had been so far off that it was ridiculous I would have dropped the whole idea. This is now enough for me to at least consider spending some money on an naval architect, test model, etc. There are still a lot of hurdles to overcome before I would ever consider actually trying to build a yacht with this system, right now this is just a fun exorcise in strange ideas.

You mentioned a problem with keeping sail shape correct. How is this different than an Aerorig with the exception that I would be power rotating the mast? (And possibly not having the jib fixed on its own forward facing boom). How did that design keep the sail shape?
http://www.yachtforums.com/forums/technical-discussion/6528-rotating-aerorig-2.html

Someone was also talking about the mast itself being strong enough, and someone mentioned spilling due to heeling and keel weight calculations. My thoughts on all this are to make this a catamaran, use an unstayed carbon fiber mast that will flex at high wind strengths to spill off excess force in a strong gust.

Any issues and problems noted from this idea? I'm pretty sure there are quite a few. I'm not currently planning to actually build this (beyond a model) so it's fine to tell me this is a hair brained idea, but if so, please tell me why. But what I would really like to hear is how to solve any perceived issues with this concept.

[amolitor]

I don't understand why you wouldn't rotate the whole assembly from the end of the boom instead of from the base of the mast.

You've already got the boom there, it's kind of inherent in the design. Why not clap a tackle on the end of it, and use the lever you've already built? I'd have to think it through, but this may actually take load OFF of the boom, so you get to built a lighter structure as well.

[Bookmaker]

I don't understand why you wouldn't rotate the whole assembly from the end of the boom instead of from the base of the mast.

You've already got the boom there, it's kind of inherent in the design. Why not clap a tackle on the end of it, and use the lever you've already built? I'd have to think it through, but this may actually take load OFF of the boom, so you get to built a lighter structure as well.

This would miss the whole point of this exorcise, which is to make a powered mast that requires no sheet. Obviously, traditional sheet and tackle works, but that's not what I'm trying to explore. I've already built several boats with traditional rigs.

Don't worry, my insanity isn't limited to this crazy idea. If I work out how to make this work, next I'm going to look into power raising and lowering the sail. If that is feasible, then next I'm going to hook the whole shabang up to a computer an have the boat sail itself. I'll tie in the GPS, wind speed and direction, and write a program that will have the boat sail itself to where you tell it to go. Now, do I think I'll actually build this as a real yacht? Well, I could win the lottery, but short of that, probably not. Would I build a model of it? Well, maybe, just to have some fun. I might even build a small boat, large enough to be fun, maybe a two person size and then I can watch it sail around Mission Bay on it's own. I can program the thing myself, but I need help figuring out the mechanics and limitations, which is why I'm here.

But telling me that this isn't the way that it's been done before is contrary to the point of this strange idea, I'm TRYING to do it wrong (or different might be a better word). I like to explore new ways of doing things, and this is my current wild idea to spend some money and time messing around with. In the end, I just want to know if it CAN be done.

[Petros]

it seems to me that unless your mast is round with a sleeve type sail (not a good shape for sail efficiency) if you allow the mast to flex to spill excess wind, it would not want to rotate very well, or it could bind up.

Cantilevered masts have be attempted, they tend to add a lot of weight. The advantage is you loose all the drag from the rigging, and one of the reasons external rigging has disappeared off of aircraft wings about 70 years ago. However on low speed sailboats the drag is relatively small and the weight and cost savings are worth a bit of extra rigging drag. I suspect that on faster multi-hulls there would be significant gains by eliminating or at least reducing the drag of the external rigging.

In your case you are attempting a cantilevered mast with a rotating base, and a motor to rotate it too. There would have to be pretty significant performance increase to justify that much weight and complication. It will be an interesting experiment.

Good luck

[CaptBill]

Have you considered instead of trying to power this motor. to instead let it be a generator of power? this power would be very large whatever it is. This power could be fed to say, the tiller, for an autopilot with alot left over. So in effect you could have, theoreticaly, a generator plus a sail that is dynamicly adjusting. You could varry the power not by APPLYING power but by CONSUMING it.

[Petros]

You would need a wind mill on a generator, not a motor at the end of a mast. Also, any wind energy you extract from the wind will slow the forward motion of the boat by increasing the drag. So while it might save fuel to use a wind mill to recharge your batteries and power your equipment, it will not come for 'free' but at the expense of higher drag.

[yades]

I believe many answers have been given by the sail & rig assembly as provided for "Maltese Falcon" conceived mainly to have a self rotational sails on a rigless mast (as conceived by Prof. J. Djikstra). If you see carfeully, the leading principle is to rotate boom and sail rather then the whole mast. Why?
Easy enough.......Because if you like to rotate the assembly mast-boom-sail then you have to envisage (as being far more efficient....) the whole structure as a "wing" and therefore to conceive a rig similar to the one applied to the AC trimaran "BMW Oracle".....a .....space shuttle of the seas....rather then a yacht ! On the other hand if we are talking ...as I presume...about .....S A I L I N G Y A C H T S as such then it is sufficient and far more efficient to have only the boom+sail rotating around a rigless mast rather then having must+boom rotating together...from an engineering point of view and for the purpose intended ......
If I may say ..... to apply a..."WING" to a "normal" sailing yacht it would be an inefficient and pointless energy consuming structure, as not only a rotational force on the mast is to be envisaged but also the gravitational forces acting offset from the mast axis when the boat is heeling over plus the very havy frictional forces to overcome on the mast base due to mast compression force acting along the vertical axis. Which material would then have to be used to withstand that situation for a long time in order to mantain the same efficiency throughout...... and what about costwise involved....and for which purpose ? :D
The ratio cost/efficiency will answer by itself....!

[CaptBill]

You would need a wind mill on a generator, not a motor at the end of a mast. Also, any wind energy you extract from the wind will slow the forward motion of the boat by increasing the drag. So while it might save fuel to use a wind mill to recharge your batteries and power your equipment, it will not come for 'free' but at the expense of higher drag.

Actually my point was this. Make her sail as if you were sheet steering like you might sail a dingy. (except the motor would be your "sheets")Instead of tiller action let the sheet out. Steer-by-sheet.This is MORE efficient. You are not restricting the air flow but the contrary. By letting the are spill in a controlled/metered way you are sailing better, on her prefered lines (maintaining heel angle), and without inducing drag from the tiller now. Power generated is from the excessive power, that which causes the rig to be over/underpowered during a puff or a lull. An autopilot that doubles as a generator when all you asked for was a sheetless rig. Plus you can take the windmill down which,yes, is inducing drag. Performance = power.

[jonr]

Sounds like an aircraft wing that has the attachment point at the leading edge (instead of closer to 1/2 of the way back on the wing).

I agree - put the mast towards the middle of the sail if you can.

[Bookmaker]

I think we're getting way off the point of this discussion. Perhaps if we got back to basics and talked. What is it that you believe shapes a sail by using a boom and sheet with a fixed mast? If you describe the basic movement that accomplishes this, then I can look at what my fixed boom and rotating mast is missing (rather than trying to change this into something else).

Again, the goal is to take away the sheet as a means to adjust the angle of the sail to the wind. Instead I want to rotate the mast. If this is going to cause some problem with the shape the sail.... why? My first concern was whether the rotation force on the mast would be too great for a motor. I no longer think this is a problem, but now I need to figure out this discussion on sail shape. I'm a little confused, so help me out with small words ;)