Block and Tackle Efficiencies

Not long ago a friend was looking to upgrade the mainstay1 block and tackle system on his sailboat.

Mainsheet Upgrade

The question was if the proposed system would provide the anticipated reduction in force. It was an interesting question that, while seemingly straight forward, does have a couple of gotchas.

Block (pulley) and tackle (rope) calculations are usually pretty simple, with the mechanical advantage (MA) idealized as:

MA = \frac{F_B}{F_A} = n

where FA is the input force, FB is the load, and n rope sections.

Calculating the total force of multiple non-colocated blocks using the same tackle presented a fun challenge that requires one to take into account the individual location of the blocks and the forces transfered.

I did not draw every single link of the block and tackle, but in general the problem looks something like this:

diagram

Considering the moment arm:

F_{L} = (F_{A} \times A) + (F_{B} \times B)

We devise these relations:

F_{A} = n_{AD} \times F_{P} \times \arctan\left ( \frac{\left |  A-D \right |}{h}\right )

and

F_{B} = n_{BC} \times F_{P} \times \arctan\left ( \frac{\left |B-C\right |}{h}\right ) + n_{BD} \times F_{P} \times \arctan\left ( \frac{\left |B-D\right |}{h}\right )

where nxy is the mechanical advantage coefficient at a given point, x, with respect to another point, y; FP is the force exerted on the tackle (which must be uniform throughout!).

Using some assumptions regarding the lengths and relative positions of the blocks greatly simplifies the calculations, and we can plug ‘n chug from there:

F_{L}=F_{P}\cdot \left ( \frac{n_{AD}}{2} + \frac{n_{BC}}{4} + \frac{n_{BD}}{4}\right )\cdot \cos{(\arctan(\frac{l}{8h}))}

As expected, there is a loss of useful force due to the ropes not being normal to the boom and that causes the boom height/length ratio to become an interesting variable in these calculations. You lose 10% of your power with a 1:3.87 ratio, 25% with a 1:7.06 ratio, and 50% with a 1:13.86 ratio.

To model a direct input (with no block and tackle), I assume that the force was applied at a point between the two blocks, A and B, and normal to the boom.

The increase from no block and tackle system to the current system (single boom aft block, A; double boom traveling block, B) is:

\frac{F_{P}\cdot \left ( \frac{2}{2} + \frac{2}{4} + \frac{2}{4}\right )\cdot \cos{(\arctan(\frac{l}{8}))}}{\frac{3\cdot F_{P}}{8}} = \frac{16}{3}\cdot \cos{(\arctan(\frac{l}{8h}))}

…assuming the boom heigh/length ratio is 7, the mechanical advantage is 1:4.01.

Moving from no block and tackle to the the proposed system (double boom aft block, A; triple boom traveling block, B) is:

\frac{F_{P}\cdot \left ( \frac{4}{2} + \frac{3}{4} + \frac{3}{4}\right )\cdot \cos{(\arctan(\frac{l}{8}))}}{\frac{3\cdot F_{P}}{8}} = \frac{28}{3}\cdot \cos{(\arctan(\frac{l}{8h}))}

…again, assuming the boom heigh/length ratio is 7, the mechanical advantage is now 1:7.02.

The mechanical advantage from current system to proposed system is: 1:1.75

\frac{F_{P}\cdot \left ( \frac{4}{2} + \frac{3}{4} + \frac{3}{4}\right )\cdot \cos{(\arctan(\frac{l}{8h}))}}{F_{P}\cdot \left ( \frac{2}{2} + \frac{2}{4} + \frac{2}{4}\right )\cdot \cos{(\arctan(\frac{l}{8h}))}} = \frac{3.5}{2} =  1:1.75

It’s not quite the 1:2 advantage originally thought, but it’s close.

Epilogue:

The bonus gotcha occurred when said friend opted to install a double boom aft block (A) and a triple deck traveler block (D), but keep the boom traveler block (B) as a double. Essentially, putting an extra “loop” just between the boom aft block (A) and deck traveler block (D).

The imbalance of tension on the deck traveler block caused it to experience shear stress and bind on the traveler rail in ways it was not designed to — not good.

Converting the boom traveler block (B) to a triple and the deck traveler block (D) to a quad equalized the tension.

Problem solved.


  1. rope from the top of the main-mast to the foot of the fore-mast on a sailing ship 

One Year Ago: Photo Time Capsule

Twice a month I get an email from Photojojo with the most interesting pictures I took from that time span the previous year last year; it’s the Photojojo’s Photo Time Capsule and it’s a great way to spend some time reflecting. For instance, May 30th of last year I was sailing in Puget Sound:

Sailboats against the Mountain
180.0 mm || 1/1600 || f/5.6 || ISO200 || NIKON D70
Bainbridge Island, Washington, United States

A few days later, I was walking around Moscow, Russia:

DSC_9015
70.0 mm || 1/125 || f/4.5 || ISO200 || NIKON D70
Moscow, Moscow Federal City, Russia


DSC_9098
18.0 mm || 1/200 || f/8.0 || ISO200 || NIKON D70
Moscow, Moscow Federal City, Russia


DSC_9184
29.0 mm || 1/320 || f/6.3 || ISO200 || NIKON D70
Moscow, Moscow Federal City, Russia

This is going to be a bitter sweet summer because for the next 8 weeks I’m going to be getting emails about how awesome my summer was last year….I better get working on making this summer amazing.

Summer Sailing Adventure

GPS data visualized using Google Earth.
GPS data visualized using Google Earth. Click image to embiggen.
Before I left on my trip, I had the opportunity to go sailboat racing with some friends on the Mata Hari. This was also a perfect opportunity for me to test integrating the Amod GPS unit (Google Maps version of the race data or just download the raw KML file.). Unfortunately, I went sailing the weekend before I left and didn’t have time to edit the photos and put them online before I took off.

I finally got around to editing them last night. Part of the reason it took so long to edit them after I got back is that I’ve really been burned out with photography and needed a break. I’ve hardly picked up my camera since I got back and almost contemplated selling it (I’m pretty sure this is a normal feeling, and don’t worry, I’m keeping it).

Last night was really fun though. I’m still not quite ready to pick up my camera, but I’m getting close. I have another couple hundred photos to edit from Edays (yes, from April…holy crap). Perhaps after that, I’ll start doing some more picture taking. In the meantime, enjoy these photos from the beginning of summer as we start to welcome our Fall Overlords.

DSC_8802
70.0 mm || 1/2000 || f/4.5 || ISO200 || NIKON D70
Seattle, Washington, United States


DSC_8811
18.0 mm || 1/2500 || f/4.5 || ISO200 || NIKON D70
Bainbridge Island, Washington, United States


DSC_8828
18.0 mm || 1/2500 || f/4.5 || ISO200 || NIKON D70
Seattle, Washington, United States


DSC_8895
70.0 mm || 1/1600 || f/4.5 || ISO200 || NIKON D70
Bainbridge Island, Washington, United States


DSC_8840
18.0 mm || 1/2000 || f/4.5 || ISO200 || NIKON D70
Seattle, Washington, United States


DSC_8926
112.0 mm || 1/800 || f/5.6 || ISO200 || NIKON D70
Seattle, Washington, United States


DSC_8850
70.0 mm || 1/500 || f/4.5 || ISO200 || NIKON D70
Seattle, Washington, United States


DSC_8884
18.0 mm || 1/1250 || f/4.5 || ISO200 || NIKON D70
, Washington, United States


DSC_8888
22.0 mm || 1/2000 || f/4.5 || ISO200 || NIKON D70
Bainbridge Island, Washington, United States


DSC_8933
70.0 mm || 1/1000 || f/5.6 || ISO200 || NIKON D70
, Washington, United States


Sailboats against the Mountain
180.0 mm || 1/1600 || f/5.6 || ISO200 || NIKON D70
Bainbridge Island, Washington, United States


Contrail
300.0 mm || 1/1250 || f/5.6 || ISO200 || NIKON D70
Bainbridge Island, Washington, United States

As is our usual agreement, the rest of the photos can be found on Flickr at: Summer Sailing 2009

Summer Wind

As July finishes up, so does my summer vacation. Less then three weeks remain before my final year of college starts. This summer has been a rather interesting one. If I had to put word to it, I’d describe it as: low-key.

Many of my friends have graduated from college and are getting jobs in The Real World©. My brother and one of my best friends are on mission trips in Europe for the summer. The dynamics have changed for sure.

That’s not to say that I haven’t enjoyed my summer. On the contrary, I love returning back to Seattle. Sailing and hiking are definitely two things I enjoyed doing and I wish I had more time to dedicate to them. I haven’t been climbing or camping yet, which is sort of a bummer. Hopefully I’ll be able to get to those before I start school.

Heads up: any outstanding chits, beers, IOU’s, etc should be redeemed before I leave Seattle on 14 August.

And guess who sighs his lullabies – through nights that never end
My fickle friend, the summer wind

And All I Ask is a Tall Ship and a Star to Steer Her By

Sea Fever
By John Masefield

I must go down to the seas again
to the lonely sea and sky
And all I ask is a tall ship
and a star to steer her by
And the wheel’s kick and the wind’s song
and the white sail’s shaking
And a gray mist on the sea’s face,
and a gray dawn breaking.

I must go down to the seas again
for the call of the running tide
Is a wild call and a clear call
That may not be denied
And all I ask is a windy day
with the white clouds flying
And the flung spray and the blown spume
and the sea-gulls crying.

I must go down to the seas again
to the vagrant gypsy life
To the gull’s way and the whale’s way
where the wind’s like a whetted knife
And all I ask is a merry yarn
from a laughing fellow-rover
And quiet sleep and a sweet dream
when the long trick’s over.

One of my favorite things about being back in Seattle are the opportunities to get out on the water. While we do have a speedboat of our own, I don’t think it get’s much better then sailing. At some point in time, I’d really enjoying sailing around the world – or at least part of the world. Although such an adventure will have to wait until I can get a boat of my own and a crew.

In the meantime, I’m fortunate to have a friend, Peter, who has a sailboat. And thus we went sailing on Monday and again on Tuesday (for the bonus round):


Remember all those pictures of your parents that you look at? This picture reminds me of one of those. In fact, I’d call this picture of Staples iconic.

All Images: Copyright 2008 Andrey Marchuk