Purchase and block friction measurements and calculations

I wanted to know the force I was applying to backstay so I did some measurements. The boat is a 35 feet C/R boat with 19/20 rig. The backstay has a 1:48 purchase with first three cascades and then 1:6. The cascades are done with 5 or 6 mm dyneema (DynaOne: http://www.gleistein.com/en-geo-yacht-productsheet-for-rope-product/dynaone) and the first block is Harken Black Magic 75 mm and the two following ones are Harken wire blocks (38 or 51 mm). Then the 1:6 is Harken Carbo 29 tripple and the line (6 mm, probably polyester) goes still through two Carbo 29 blocks (about 90 degree bend in both). All block are ball or roller bearing blocks and they are working at less than half of the maximum working load.

I measured the stretch of the first cascade (5 mm DynaOne) and it was about 0.6% which should be equal to 10% of the break load, thus about 250 kg. So the force on the backstay is about 500 kg, which is quite surprising, since I was pulling the line very hard and with 1:48 I was expecting to get at least 1000 kg.

Then I measured how hard I was pulling. Unfortunately I only had a 40 kg scale and it run out of scale after I had pulled about 6.5 m of line and the maximum was 8.5 m (with 0.6% stretch). I think I'm pulling at about 50 kg at 8.5 m. Then I also measured the load needed to keep the line in place or the load at which the line is slowly releasing. They seemed to be about the same and were about 8 kg at 8.5 m.

Thus I only have a 1:10 purchase while pulling and about 1:60 while holding/releasing instead of the theoretical 1:48!

I also tried to calculate with some friction. Assuming the friction is linear to the loading of the block (not line!) I got the following:

Pulling at 10% friction
Backstay 500 kg
First cascade 500/2 + 500*10% = 300 kg
Second cascade 180 kg
Third cascade 108 kg

1:6 108/6 + 108/3*10%*6 =39.6 kg

First 90 degree 39.6 + 39.6*SQRT(2)*10% = 45.2 kg
Second 90 degree = 51.6 kg

So that's it! Isn't 10% quite much friction for a good quality block?

The same calculation with 5 % yields only 25.4 kg, but still only 1:20.

Calculating the holding releasing was less successful:

At 10% friction:

Bacstay 500 kg
First cascade 500/2 -500*10% = 200 kg
Second cascade 80 kg
Third cascade 32 kg
1:6 32/6 - 32/3*10%*6 = -1.1 kg

At 5 % friction
1:6 3 kg
After 2*90 degree 2.6 kg

Thus even at 5% friction the calculated value is smaller than the measured.

 

IMHO the 6:1 purchase sheaves are too small (~5:1 sheave to line). Yes I know that Harken says that 6mm is the MAXIMUM line size, but falls work much better with a sheave : line of ~10:1. FWIW, the recommended sheave: line ratio for things like crane falls is 18:1. Also the typical rule of thumb is that you lose ~10% of line tension for every 180 degree turn. The effect of the friction coefficient (f) is to make the driven radius appear longer (i.e. Tin*r = Tout*r*(1+f) )

 

Actually Harken says 8 mm is the maximum line size: http://www.harken.com/productdetail.aspx?id=4532&taxid=416

Do you think going to 5 mm line would help considerably? Or is the only solution to go for bigger blocks? How much does the line quality matter? It needs to work with a cam cleat and be nice to hands.

 

You can really damage a high modulus line by bending it over a a too small sheave, and a triple with 3x180 wraps even with a hand soft 8mm line would approach the Carbo SWL of 990 lbs (i.e. 990/6 = 165 lbs = 735N...or 75 kg force which is not much pull.

http://www.neropes.com/linecare.aspx

You could do a stripped core ( http://l-36.com/DB_C2_StripCover.pdf ), or a Harken magic box on one end...don't know what the space is and if double-ended is a requirement. Its funny, but I'm about to refit my Catalina 22 backstay adjuster and will be doing pretty much the same thing this weekend. but I most likely will just do a typical 4-part single ended.

<shrug> After you stuff the bow the first time you will shake the falls even so you might have to take it up several times...maybe just deal with it.

 

If it was me I'd take the whole thing off the boat lay it out on the floor, connect a load cell to replace the backstay, pull the other end and see what I get. Every time I've done this I've been amazed on how inefficient tackles are.
FYI Harken Magic Boxes are about the worst, about half the power is eaten up by friction.

 

I'm not going to go for a thicker line, 6 mm is still OK to my hands. Stripped core is not an option, since there is not much line left when pulled to maximum and this is a double ended system. There is no need to have a high modulus line in the 1:6 tackle.

Actually I'm quite happy with the system. I get enough forstay tension. Of course it would be nicer, if I had to pull just 25 kg instead of 50 kg. But it is OK since I have a good pulling geometry at the steering position. Also it would help, if I could get the same force with e.g. 1:32 or 1:24.

I don't have a 1000 kg load cell, thus I can't measure more accurately. But I think measuring the DynaOne stretch is at least +-20% accurate, which is enough for this purpose.

 

The accurate way is to borrow a large dynamometer and install it between cascade and backstay proper.
All the sophisticated calculations are dependent on SERIES of factors (like friciotn coefficients of blocks, which are in themselves dependent on line type, line diameter, the load at the moment, direction -i.e. is the line pulled or released, etc. ), most of them guessed or assumed and therefore end result is not accurate by definition.

 

Certainly using a load cell is more accurate, but note that I measured the force on the backstay from the stretch of the dyneema on the first cascade. There are not much assumptions needed, since the stretch of the dyneema is given by the manufacturer and it was quite linear from zero to that load.

The other part was just to measure the efficieny of the tackle. Most sailors think they will get 2000+ kg from a 1:48 tackle by pulling 50 kg. Some even thought i would overstress the 6 mm backstay (3000 kg breaking load).

 

The stretch is not that big in absolute terms.
So the error of some ~10% in measuring the stretch alone would not surprise me. (the stretch measuring method was not described here)



The biggest uncertainty is the friction in all the blocks however.
And this friction is a function of block (type, condition, load acting, whether load is applied or released, etc.).
And at each step of a cascade those uncertainties are adding up, increasing the resulting error cumulatively...


Edit.

Direct measurements are simply more reliable, that my point is.
Whenever possible, I would go for direct measurement.
To find a dynamometer with a few tons capacity should not be unsolvable problem.

 

The stretch was measured by attaching a 2 m steel measuring tape to the DynaOne line of the first cascade. The total stretch was 12 mm and it could be easily read to +-0.5 mm, since there was a sharp edge for accurate measuring.

Only the fiction of the first block can alter this measurent and you could get 11-13 mm depending on how the block was balanced.

The tackles after the first cascade and their friction determine the force needed to pull the line, but that's another story and has nothing to do with the stretch of the first cascade line.

Since I was mostly interested in the applied force on the backstay, load cell would not really help. I could measure the tackle on the floor, but that would only give me the efficiency of the tackle, not the force I will have on the backstay. And that efficiency can change a lot when put back to boat with always a bit different angles etc.

I could also put the load cell between the tackle and the backstay, but then the backstay would be a bit longer and I would need to modify the tackle, which now is used all the way it can go for the maximum force.

I could also measure the distance between the backstay and some point on the boat and use a load cell + some tackle etc. to pull the backstay to same position.

All of these sound more complicated and I don't really need more accuracy. I just wanted to know that I'm not pulling 1000+ kg, which would have been way over the Selden recommendation of max 20% of backstay breaking load, which is 31 kN * 20% thus a bit over 600 k.

 

Nice experiment Joakim. Quite a surprising friction indeed, if it is 10% per block. Why do you think the result is so different for the releasing case calculation?

The 500 kg should be rather adequate for your boat, our boatbase would give 580 kgf for a 1% sag on the forestay.

 

Blocks are not that great efficiency-wise, but 10:1 actual out of 48:1 theoretical can be improved on. Post photos.

I'd guess about 70-75% for the 8:1 cascade and 30-40% for the triple. Which suggests you could drop to a 4:1 if you could get the efficiency up to 50-60% and not have any higher pull, just less length to deal with. For comfy hand lines, keep your gain small. The gain should be in the Dyneema. Can you make the last cascade a 3:1 and just use 3:1 for the final? Or will you bottom out? That's only 36:1 total, but the efficiency should be better.

 

The last tackle needs to be even number thus 1:2, 1:4 or 1:6 in order to make it possible to have it double ended.

The range is 8.5 m line, thus the backstay moves 0.18 m, the first casade 0.35 m, the second cascade 0.71 m and the last cascade (thus the triple carbo 29 block) 1.42 m.

The space needed would be the sum of all these plus some space for blocks, about 3 m in total. The first block is about 4 m from deck, thus there is plenty of space for this tackle, but not for another cascade, which would add about 1.5 m. Probably not even for making the last cascade 1:3.

Mikko I don't know why the calculation is so different for the releasing case. Maybe there are some non-linear friction or maybe not all blocks are moving for the rather short releasing distance I was measuring. Of course there can also be an error in my calculations.

 

That would be tight. I don't know how close you block your triple, but a 4:1 double tail can be set up to run very short. It looks like there is enough, but just barely. Ie, 2:1, 2:1, 3:1, 4:1.

Are all the wraps 180? Or is there a bit of splay. How much splay when she's all the way in?

As far as the difference in friction for release, many blocks use a combo of bushings and bearings. The bushings are higher friction and take over in high load cases. The bearings are for low load and freespinning, specifically to improve the outfeed of tackles. So some of the sheaves in the triple are probably running on their bearings as you pay line out.

 

Here is a picture of the upper part obviously not showing the first block. The 1:6 tackle has a triple carbo 29 also on the other end, but only two blocks of it are used. Then there is a double carbo 29, which leads the two control ends forward with about 90 degree angle. Then there is a pair of single carbo 29 that also have a 90 degree angle. On port side next comes a carbo cam cleat. On starboard side there is still one carbo 29 with 90 degree bend and the the carbo cam.

Thus on the 1:6 tackle there are five 180 degree wraps and then two 90 degree wraps on port and three on starboard.

Going to 1:4 would make that 3 + 2 or 3. Maybe there is enough space for 1:3 of the last cascade (haven't been to boat to measure), but is it worth the trouble.