Ox logging and ground skidding draft measurement video

Great job Tim.
It is nice to see that the method of least force is also the better way to keep a saw log clean.
Erika

One of the interesting things about this group of measurements is that as all three of these twitching methods are applied to the front end of the log, one could assume with some confidence that the drag on the rear of the log remains constant. This allows one to tease out the relative contributions of the front and rear of the log towards total draft. Perhaps this will be interesting…

One could model the total drag on the log as the weight of the front end*friction+weight of rear end*friction. Previous work from Tim shows that stoneboat friction is approximately 0.4x weight. I think this is a good approximation of friction at the rear of the log, which can slide over ground without digging in and tilling it. For this particular log, this would be 1050/2*0.4 or 210 lbf (I am assuming the rear and front halves are approximately the same weight). With a sled under the front end of the log, the average draft is 392 lbf, with only 182 lbf coming from the front end (392-210). One might be surprised that the draft of the front end here is lighter than the rear. I think this is totally due to the angle of draft. The vertical component of a 10 degree angle of draft with a total force of 392 lbf is about 68 lbf (sin10 degrees*392=68). The vertical component would reduce the total applied weight of the front end of the log from 525 lb (1050/2) to 457 (525-68). 457*0.4=183 lbf, which is damn close to 182 lbf.

So, the drag applied by the rear end of the log in this case is about 210 lbf. As the front of the log does not physically lift of the ground in any of these pulls, and the geometry of the rear of the log remains constant, the drag applied by the rear of the log would be the same (210 lbf) in these different situations. I am going to assume the angle of draft also remains constant in these situations. That means the applied force of the front end is sin10degrees*total draft in all cases (which is 92 and 97 lbf for the tongs and chain respectively).

Here’s where the differences really stand out. The average force of the log skidded with tongs is 530 lbf and the chain is 546. That means the drag from the front end of the log is 320 lbf and 336 lbf, respectively. These represent friction coefficients of 0.74 (320/((525-92)) for the tongs and a whopping 0.78 (336/(525-97)) for the chain, which is almost double that of the sled or the rear of the log. Pretty dramatic difference when you dig into the numbers.

I think this is also a great illustration of why getting lift on the front end of a log is important. Actually, these numbers give is a way to determine the optimal amount of lift to apply to this particular log in these different situations. To do this I determined the upward vector of the total draft at 10 degrees, as I did previously. This gives the downward force at the front of the log (525-sin10degrees) and horizontal component of the vector that must be exerted to overcome drag in the front end which is equal to the downward force times the friction coefficient (0.4 for sled, 0.74 for tongs, and 0.78 for chain). The horizontal component of the rear of the log we already know will always be 210 lbf, so we add the horizontal frorce vectors together and use trigonometry to determine the total force vector. One can then use excell to plot all required draft forces at these different angles and get an idea of the ideal angle of draft for these different situations (I have attached the plots below). Interestingly, the optimal angles are not identical. One can tell from the plot below that a sled isn’t very sensitive to draft angle, but is the angle is optimal at about 20-25 degrees. The tongs and choker chain are much more sensitive to draft angle with an optimal angle of around 35-40 degrees. As this angle is probably not achievable with standard hitching methods, the recommendation would be to hitch as short as possible if you are using a chain or tongs. Or you could simply use a sled and not have to worry about angles and such. I think we already knew this, but it’s nice to see the math too.

Interesting stuff, and fun to think about! 🙂

PS. This post contains substantial edits from my previous post due to a few math errors… These were actually pretty important math errors and they changed my overall conclusions.

Hey, who’s calling me a nerd! Need I point out the you just performed calculus on a trigometric function, and in public??? 😀

Thanks for the thoughts, numbers, and math, Tim. It is interesting that we come up with functionally similar angles using different methods. Getting similar answers with different methods definitely gives more confidence. I am probably picking a nit, here, but I like an analysis that treats the front of the log differently than the back of the log because the front can dive into the ground and till while the rear cannot. Because of this fundamental and important difference, I think the friction coefficient for the front of the log will be different from the rear. Also, I don’t think that a lift to one side of a log will necessarily shift that same weight to the rear. A lift of 525 lbs on one end, for example, doesn’t make the other end weigh 1050 lbs… So, I’ll rework this with the additional information. I kinda wonder why, because I’ll probably end up with the same take home information as in our previous two posts, but let’s see…

Sled: As the front of the sled can’t till and the rear of the log is off the ground anyway I’ll estimate draft without reguard to front and rear ends. For a pull of 392 lbf at 15 degrees, the horizontal component is 379 lbf (cos15degrees*392), and the vertical component is 101 lbf (sin15degrees*392). The vertical component removes 101 lbs from the weight of 1225, yielding an applied weight of 1124. This gives a friction coefficient of 0.34. with this friction coefficient, one can plot the resulting forces (shown in the graph below). I get a minimum draft force at 19 degrees, which is damn close to Tim’s 18 degrees, but what really jumps out at me in this plot is just how flat it is. All resulting draft forces from an angle of 7 degrees to 29 degrees are within 2% of the minimum. So, for all practical purposes, the angle of draft doesn’t matter for a sled.

Tongs: I am going to model the rear of the sled as having a friction coefficient of 0.4 (slightly more than the sled) because it can’t till and has a rough surface (and because I’m a stubborn bastard). The downward force of the rear half is still 525 lb, resulting in horizontal drag is 210 lbf. For a pull of 549 lbf at 15 degrees, the horizontal component is 511 lbf (cos15degrees*549), and the vertical component is 137 lbf (sin15degrees*549). The vertical component removes 137 lbs from the front weight on 525, yielding an applied front weight of 388. As the horizontal component of the pull is 511 lbf, and the rear takes up 210 lb of this, the resulting friction coefficient is 0.78. Wow, can the front dig in! With the friction coefficients of the front and rear, one can plot the resulting forces (shown in the graph below). I get a minimum draft force at 38 degrees, which is a ways away from Tim’s number due to substantial lift on the front (not the rear) of the log. This probably doesn’t matter is practice, though, because either angle is challenging to achieve. Here the graph illustrates how much more sensitive this setup is to draft angle, with a 2% increase over minimum draft at 27 degrees, a 5% increase over minimum draft at 20 degrees, and 10% increase at 13 degrees.

Chain: similar to the tongs, I am going to model the rear of the sled as having a friction coefficient of 0.4. The downward force of the rear half is still 525 lb, resulting in horizontal drag is 210 lbf. For a pull of 565 lbf at 15 degrees, the horizontal component is 546 lbf (cos15degrees*565), and the vertical component is 146 lbf (sin15degrees*565). The vertical vector yields an applied front weight of 379. As the horizontal component of the pull is 546 lbf, and the rear takes up 210 lb of this, the resulting friction coefficient is 0.89 for the front end of the log (which is similar to the friction of a car tire on pavement). Wow again! Just as in the other examples, I can use the friction coefficients to plot total forces at different draft angles. For the chain, I get a minimum draft force at an impractical 42 degrees. This type of hitch is even more sensitive to draft angle, with a 2% increase over minimum draft at 30 degrees, a 5% increase over minimum draft at 23 degrees, and 10% increase at 16 degrees.

Draft buffer post #26 has made me think a lot. One of the things that this brings to mind is that we have been modeling the soil as an incompressible substance, even though we know better. Now when I say compression here, I don’t mean irreversible compression, just the “give” that you feel when you step on soil versus say concrete. I think this is an important factor, and here’s why. I think Tim is right when he points out that my friction coefficients for the front of the log are too high to be reasonable. And yet experience, observation, and Tim’s tractor+sled data (post 26) would indicate that weight in the front somehow causes more drag than weight in the back. If one doubts this, one can also look at the wear on sled runners. I have had to replace mine several times, and the most wear is invariably at the leading edge of the runner right where soil contact is made. There’s a good bit of wear at the very rear of the runner too, but the middle of the runners always holds up a lot better. Now every part of those runners sees exactly the same terrain, travels the same distance, and is made of identical materials, but the wear pattern is dramatically different. On my sled, I bet the leading edge wears at twice the rate of any other area. Maybe even more than twice… So, because the friction coefficient is probably almost the same (soil vs steel), there must be more weight on the leading edge somehow. With even or variable loads, that can’t make sense without some degree of soil sinkage. With soil sinkage, the front of the sled would be thrust up onto upcompressed ground and be briefly suspended between the leading edge of a flat runner and the trailing edge. At this point, weight from the front half of the sled will compress the soil along the leading edge, and the trailing edge will sit on already compressed soil at the rear of the sled. The elevation of the sled’s front may or may not be noticeable (just like you can’t always see the front of an icebreaker elevate) but the concept of “lift and fall” still applies.

So, I’m going to see if vertical lift and the work of compressing soil can account for the increased drag from the front of the sled in this test (and see if this also works for the sled in draft buffer post #26). During the “lift” component a pull into compressible soil with a flat bottom sled, all weight will be suspended between the leading sled runner edge (or other contact point) and the trailing rear edge. The downward force on the leading edge has to overcome the compressibility of the soil at a rate proportional to the angle of the leading edge. Half the load in Tim’s example weighs 613 lbs (1225/2), which is elevated by the the 15 degree total pull of 392 lbf. The vertical component of this pull is 101 lbf, leaving 511 lb on a 10 degree incline (estimated angle of attack) and a horizontal pull of 379 lbf. Moving 511 lb up a 10 degree incline takes 89 lbf along at a 10 degree angle. That equates to a 90 lbf horizontal pull. So 90 lbf out of 379lbf might used up compressing soil along a 10 degree leading edge of a sled. That leaves 289 lbs remaining. There is still 511 lbs in the front and 613 lbs in the rear, which if applied equally would yield friction coefficients of 0.26. Now these friction coefficients are really quite low, but this is analysis models this interaction as non-compressing, non-tilling, and smooth, and takes the leading edge into account separately, so maybe this isn’t stange… Overall, using this analysis the front edge is responsible for about 60% of the draft and the rear is responsible for about 40%. This general pattern explains some of the patterns seen in post #26, where loading up the front of the sled resulted in higher draft forces than loading the rear. It’s really pretty tough to do these analysis in great detail, because so much depends on the exact angle of attack at the leading edge, the length of the sled, and soil properties (such as compressibilty and dampening). Because of these complications, I can’t compared exact numbers, I can really only see if the trends match, which they do.

There are practical applications of this modelling. One aspect that comes out to be important is how critical a shallow angle of attack is on sled runners. Also, it would be advantageous to extend the runners out in front of the load so they are not as weighted while they are being “lifted.” Lastly, having a very shallow rounded bottom to the runners (very slightly higher in the middle) will prevent much of the the deleterious loading of the front end. I bet a runner such as the top runner in the photo below would be much more efficient than the runner below. Maybe as much as 10% improved with respect to draft for a given weight… Now, there’s something to test! 🙂

Sorry Erika,
sometimes I get excited and do a bunch of modeling, thinking, and writing and don’t stop to explain why I’m doing it in the first place…

Basically, I think that Tim’s data in this post and others can be partially explained by having greater drag from the front of the sled or log than from the back. I think this makes some intuitive sense and matches with experience and observations but it is difficult to explain exactly why that is. I am interested in trying to figure out “why” because whatever is causing the additional drag might be able to be “fixed.”

Most of the math is me coming up with theories of what might be causing the additional drag in the front, and seeing if this math matches with measured values. The idea is that if the math predicts values that are far from the measured values, than the model/theory is probably wrong. I created a model based on different coefficients of friction that explained the values in this thread alone. Tim pointed out (very gently I might add) that although it does match the value in this post, the coefficients of friction are hardly believable and it the model doesn’t match measurements in post #26 of the draft buffer thread. So, I came up with a different way to explain exactly how the drag might be higher in the front than in the rear, based on the compressibility of the soil. I think it makes sense, and explains the data in this post and most of post 26, but we’ll see what people have to say… It sounds like whatever the explaination is, it is probably going to be somewhat theoretical. That’s what’s nice about the sled runner shape test. If a theory can’t be tested somehow, there’s no way to know if it’s true. Also, the runner design is a practical application of the concept, if it does indeed work. There will probably be some batting back and forth of ideas to come, that is if anyone else wants to be nerdy.