Aspect ratios

Footy Class General Discussion (Footy)
1

Why is it that people’s Footy rigs are of such extraordinarily low aspect ratio? Is it that they look at the B/Storm/Silly Rig and mimic it? Are they afraid of raising the centre of effort?

I say this because at Birkenhead the Mighty Moonshadow (:devil3::devil3: - you pull my leg Mark the Moth and I’ll pull yours) had an A2 rig (i.e. over 305 mm but not the full Monte) with a markedly higher aspect ratio than any other boat. I have no idea whether it was actually doing much good - but given the way the boat was going to windward, it can’t have been doing a lot of harm either.

If you sit down with an O-level (approx 10-11 grade) geometry textbook of 30 years ago to tell you how to do the - very easy - calculation, you will find that the centre of area of a triangular sail does not move upwards very much as the rig height increases. If you can avoid the excesses of any Cookes spoiling the broth, rig weights are such that the loss of stability on that score is minimal. But the improved lift/drag ratio of the higher aspect sail means that it has lower heeling force per unit of forward thrust.

Unfortunately the magic numbers (coefficients) that make it possible to work out just what the best answer is seem to be largely the closely guarded secrets of big-boat designers, sailmakers and spar makers.

Do any of you flying types have any ueful insights?

:graduate::graduate::zbeer::zbeer:

2

Angus,

both of my rig, one 32" and the other 21" (507 derivative) are what I would consider high aspect ratio…no bowsprit and the main boom stick out past the stern of the boat about an inch or so…

the 32" is great in very low 0-3 winds anything higher its juts too much… the 21" is good for 0-3 great for 3-5. over 5 and she get over powered. I feel that if I kept the same sail area and brought the rig lower lets say closer to 15 inches. I think it would sail better in the higher winds… which means I’m really just moving the sail area lower to the water were the winds are slower.

I’m still toying with the modified hoyt rig…

3

Angus,
There is a great picture on “Photobucket” that I think Andrew H took showing your Moonshadow sailing next to Bill’s Razor 3 carrying one of my low aspect ratio McRigs (#427). Both boats seemto be pointing the same although the Razor is carryying more sail and has a greater angle of heel.

I started out with normal sorts of aspect ratios, but since I found that the limiting factor in how much sail area Footys could carry was stuffing the bow under downwind, I started experimenting with lower and lower aspect ratios. This is also why these sails don’t carry fat (or even square) heads. I am trying to keep the CE as low as possible.

It also has a lot to do with where I normally sail. I normally sail in small ponds with pretty flat water, not the North Atlantic gale conditions you seem to favor. Downwind, the low boom seals off the foot of the sail and as the boat pitches forward, the foot even rides along the surface, preventing the bow from digging in further. I don’t expect this would work in England!

The only times that these rigs have been beaten in the US over the past three years was twice when my conventionally rigged AF with square topped sails won in conditions much like yours. Upwind, the main could be twisted off and downwind the jib could be hidden behind the main.

It is probably too early to read much about the rigs into your win as it was a very high tech Moonshadow going against a very low tech Razor. Let’s wait till the next generation of foam Cobras with carbon keels get some races under their belts.
Scott

4

I will have to agree with Scott here for the most part.

A high aspect ratio sail, even if your boat’s heeling is not much effected by the height, and even if it is so much more efficient upwind that she can carry less sail area and still go great guns, the fact is that the high aspect rig still only has 4 or 5 inches of boat in front of it going downwind where a superior airfoil profile doesn’t do squat for you. Downwind sailing is the wind pushing your sails/boat in the direction it is blowing so there is no advantage to height, in fact, to reduce the tendency for the bow to bury one wants as little lever arm as possible looming over the bow.

Footies are generally terrible at sailing downwind. They are pretty slow in comparison to other, longer r/c sailboats and have all sorts of control issues when the wind picks up. They sail bow down a lot of the time and with the nose buried to some degree broaching or pitch-poling happens much faster and usually catastrophically. A high aspect ratio rig amplifies these running deficiencies.

On the other hand I don’t agree with Scott’s low to the deck approach either. The wind right at water level is very turbulent, shredded and influenced by the drag induced by the boundary layer. That is why I mount my rigs on the raised deck of my angled/diagonal designs. This in turn makes for rather squat squarish sails, low aspect by Angus’s standards.

But thats okay because I don’t see the advantage of the truly triangular sails for Footy size boats. To me, most of the triangular sails on these small boats look like the tops of the sails on any of the larger classes. Those triangular tips don’t contribute to lift upwind because they don’t have enough chord length to establish an airfoil section or attach airflow. They function only for aesthetic purposes, to make the sails look like scale big boat sails (and add drag at the top).

Fat head type sails can carry a proper airfoil shape over the entire length of the sail, doing away with the draggy, pointy tip. But because they carry a broader chord at the top of the sail they have to be shorter so that they don’t increase the leverage on the bow downwind. So, in effect, fat head sails give the lift advantage of the high aspect ratio sail upwind while attempting to reduce the nose diving propensity of Footies downwind. That is why I favor them.

One other thing I want to point out. I would not read too much into Moonshadow’s win at the EuroGP. Moonshadow is an old boat, she has been hanging around for a while without doing much more than average placings. Her victory at the EuroGP is more likely a concurrence of a competent, experienced skipper, sorting out of the details over the years, and the perfect wind/weather conditions. My very light M Class boats reveled in the conditions that were at the GP (or at least how the race reporting described them). I also know what it feels like to be on a multi-season winning streak with a boat that I designed, so I don’t fault Angus for his elation at seeing one of his designs (and the first test bed for his immersed stern theory) do well finally. The test though is to see if the combination of skipper and boat is more than a one-trick-pony. Beat Roger Stollery sailing his AWK or whatever his latest creation is and then I will be impressed. Then I might have to re-evaluate my opinion on immersed stern theory.

5

Neil, that shootout is arranged for the UK IOM Champonships the weekend sfter next. Both Moonshadow and the AWK will be sailed by an ex-IOM world champion, so there are few if any excuses going.

:zbeer::zbeer::zbeer:

6

I wish you and your Moonshadow well. I am sure it will be interesting!

7

Angus - one other thought, I would suggest that the respective skippers swap boats in alternate heats so that sailing skills are balanced out as much as possible and do not have undue influence on evaluation of the hull designs.

8

Hi Angus,

There is no question that higher aspect ratio aerofoils have lower induced drag. THe question with the Footy is whether the reduction of drag would be significant with a Footy. With such high cambered aerofoils the lift will be high but also the drag. Also all of the rigs are actually low aspect ratios in aerodynamic terms.
What might be interesting is if the taller rigs get into higher velocity air.
I did a quick spreadsheet calculating the Specific Wind Power in the heights suitable for a Footy. It is interesting to see how low the available power is. I didn’t really have a taller rig to input its chords but you could play around with figure to see if there is any advantage. It looks that if there is an advantage it will be small and still has to be countered by the additional height of the centre of effort.

Regards
Peter

9

Oops,
Spreadsheet this time.
You need to have a wind speed to enter in the sheet.
I put it at 2m as this is approx. the height our hand held Dyer meter would measure at. Also it is calibrated in Knots.

Regards
Peter

10

If I am interpretting the spreadsheet correctly, the majority of the force available is well within the range where a 30.4 cm rig (the “old” small rig) would provide all the force needed for a Footy. Merely increasing the total area in the small rig would compensate for any loss that might be incurred by not using a high aspect ratio rig. If the benefit derived from a low aspect rig are seen as reduced ‘submarining’, then all footy rigs should have short masts.
I had always been led to believe that the wind velocity increased only slowly with height above the water surface, yet the spreadsheet seems to show that most of the reduction in wind speed occurs below 15 cms ( 6 in. ).
Or am I wrong?

11

There is some experimental data available. Rod Carr made some measurements, using drooping ribbons attached to a pole in the middle of a lake. I think it was published in the AMYA magazine about 2 years ago. As I remember, he was trying to correlate low level wind speed to the typical weather service prediction, which is at about 30 ft altitude. He found significant wind speed diferences up to 10 feet or so (feel free to correct me if my memory is erroneous).

Also, as Angus has mentioned, there is significant degradation in lift/drag ratio as aspect ratio is reduced. The lift/drag ratio impacts pointing ability. In airplanes, it is even more critical, as it impacts fuel consumption. Most airfoil test data is at very high Reynolds numbers (for aircraft or big sailboats), not applicable to Footy sails. But I have seen some recent data, at low Reynolds numbers, which indicates that it doesn’t degrade too much until you get below an aspect ratio of 1.5 (the data shows it gets much worse at 1.0, but no data between 1.0 and 1.5). I have noticed that most of Scott Spacie’s sails appear to have an aspect ratio of about 1.4, which may be the sweet spot.

12

Hi Rod,

The formula for the specific wind power in watts per square metre

Power = 1/2 x p x V^3 (W/m^2)

where p is (rho) = density of air (1.21)
v^3 = velocity cubed

The velocity at a given height is

V unknown/ V known = (height of unknown velocity/height of know velocity)^n

Where n = the power law exponent of the surface roughness Z0

Z0 for water is given as 0.0002 by the European Wind Atlas

power law exponent = =-1/(LN(Z0/15.25))

This should give a logarithmic curve.

This all gives the theoretical power in the air mass but not all of this power can be extracted.

Sorry this interface is definitely not meant for formulas.

The spreadsheet was done in a bit of a hurry so I don’t guarantee that I didn’t make a mistake. I just thought it was something to consider re the height of rigs. I’ll have another look and perhaps add a graph.

Regards
Peter

13

Hi Rod,

I think your reading of the sheet is correct. The wind speed at the surface of the water is zero. It rapidly increases until eventually reaching a point where it doesn’t increase any more. This is at the end of the Atmospheric Boundary Layer, which is high 500m or more. Most meteorological wind speed measurements are done at 10m. I have attached a new version of the spreadsheet with a graph. Basically Footys are right where the action is.

Regards
Peter

14

It also suggests the interesting idea that the same sails, but mounted on a higher mast, would have much increased driving force. Which also suggests that Footy sails should be inverted, with the boom at the top of the mast, and the peak at the deck level.
What I’m getting at here is that the lower parts of the sails, which traditionally have the greater area, are essentially wasted, just so much dead weight. Of course, excess heeling and submarining have to be considered too.
It seems that like everything else in Footydom, some revised thinking about the basics is required.

15

Something like these two, maybe?
This approach might also work for rigs for boats that fit into the “box” at some more extreme diagonal?

16

Would the objective be to reduce mass in the sailset by curving it in at the bottom rather than coming straight down to a flat boom? Other than reducing overall boat weight, does this help with tacking or somesuch?

-Rick

17

Purely to get the available sail area up into the region of more effective wind force, while reducing the least effective part of the sail, which does contribute to the overall weight.

18

Some of the stuff on here about aspect ratios is oversimplified. A large “span” (in our case luff length) allows reduction of induced drag. For a given area, a high aspect ratio has a longer luff and therefore lower induced drag. Of course if you go higher, you’ll heel the boat more, so it’s necessary to compromise. For hulls like most footies that are hard to drive, power trumps efficiency. But you can’t entirely"make up" for the lower efficiency with more area, at least not when close hauled, where pointing ability is important for speed made good to windward. Especially when all the boats are close to hull speed and heavy enough to be unable to exceed it without an awful lot of power.

Some formulas:

lift=Cl1/2fluid densityv^2area
drag=Cd1/2fluid densityv^2area
Note that there are other sources of drag besides induced drag. Note also that lift is perpendicular to wind direction and drag is parallel to it.

induced drag coefficient:
Cdi= Cl^2/(aspect ratiopie) where e is a factor relating to span efficiency, i.e. how well is the lift distributed? If I recall correctly, this was first worked out by Prandtl in the 20’s or 30’s. The guy was a genius, I think.

Ideally, you want an elliptical lift distribution over the span, which is why triangular sails aren’t the greatest thing. Note that elliptical lift distribution is NOT the same as an elliptical shape. Also, this all gets complicated by what goes on at the bottom. If the hull is like a plate sealing off the end of the sail, it will raise the effective aspect ratio considerably. On a very wide hull and with negligible variation of wind with height, this would almost double it. However, you need a very small gap to get the full effect. And we get considerable variation of velocity with height. On the other hand, a triangular sail might make up for this effect. On an airplane, span efficiency might be around 0.7 to 0.9, but I bet it’s a lot less on a sail.

If you note that AR = span^2/area, then do some algebra, I think you will find that:

induced drag = (lift^2/span^2)/(1/2v^2density)

and the AR drops out. However, if the AR is low so that you have extra area you will have more frictional drag even if you’re not getting much lift out of the area.

I don’t know if that makes things clearer or muddier.

19

There are sail materials you can use that are fantastically light. Take one of those vegetable bags from the supermarket, which I’m guessing have comparable area to a footy rig, and drop it. It will take a long time to get to the floor. I think the stuff weighs on the order of 5 grams or less per square meter (about 1550 square inches, as I recall) . I don’t know what people are using for footy sails, but I’m sure they don’t have to weigh much. 200 square inches of a one ounce fabric is still only 4.4 grams!

20

BTW, that info about wind velocities with height is great! Thanks.