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*To*: dinosaur@usc.edu*Subject*: Rex Towing Capacity (Aaargh!)*From*: ngear@gvtc.com*Date*: Wed, 25 Feb 1998 15:39:03 -0500 (EST)*Reply-to*: ngear@gvtc.com*Sender*: owner-dinosaur@usc.edu

At 10:24 PM 2/24/98 -0600, Jack Conrad wrote: >...A very useful post sent >by Nicholas (Wren) (thanks Nicholas) suggests that GSPaul's estimation of >a two-ton powerlunch was not impossible for a _T. rex_ (something I had >never bothered to do the math on). Nicholas' analysis of the ability to >drag a four ton ceratopsid was very logical, though I'm not sure that his >conclusion was accurate... To quote Homer Simpson... DOH! It seems I can't get one foot extricated from my mouth without inserting the other one in the process. In my last post I showed how a rex would indeed have been able to load-compensate GSPaul's Big Happy Meal (which I had been so publicly skeptical of) and then mentioned how this process could be applied to calculate the rex lifting capacity of any sort of load. So far so good. Then I applied this argument to the thread debating whether the tooth marks in the ceratops frill were made pre or post mortem (the post mortem argument being that the rex was relocating the corpse). I showed the rex could not have had sufficient lift capacity at its head, did a bit of hand-waving, and congratulated myself that I had dispatched the relocation scenario. More fool me. Jack is quite right, of course. My argument was both logical and completely irrelevant. I figured rex lift capacity correctly (I think) but then utterly failed to calculate rex towing capacity--which would have been the most likely way a rex would relocate a corpse (ie. drag it). I basically proved the improbable impossible. (And for my next magical trick, I will show conclusively that the rex definitely could not have ridden a bicycle.) Okay, so here's the question. Could a rex have generated enough towing force to drag a ceratops? Right off the bat, we have a problem in that we don't know the coefficient of drag for a ceratops, but I don't think this will matter much. If we can show the rex could have gotten it moving, we can be pretty sure it could have dragged it, so let's just figure what the rex would have been capable of first. To know how much pulling force a rex exerts, we need to know three things. We need to know the weight of the rex, we need to know the angle from the foot to the hip (I'm fudging a little here, this assumes the hip was normally over the foot, which it wasn't quite, but close enough for us), and we need to know the angle from the bite up to the hip, and we can make pretty good guesses about all of these. Now, we can figure this formulaically or graphically. Since we are just estimating (and I'm already fudging details anyway) the latter approach is plenty precise enough, it's lots easier, and it's more intuitive. We just draw a load (vector) diagram and measure. First we represent rex's weight. This is a down force of (say) eight tons, so we make a vertical line eight units long (any units, just remember that one unit equals one ton). Cancelling the vertical weight line are two support components. One will be the legs and the other will be any side force (ceratops drag resistance in this case). The leg component starts at the foot of your vertical line and goes up at the angle from foot to hip. (With zero side force, the leg component is also vertical and eight units long.) The side force starts at the top of your vertical line and goes up at the angle of bite to hip until it intersects the leg component. Then all you have to do is measure the length of the side force vector and you have your towing load. Let's try it with an extreme case of rex's legs angled back at 45 degrees, and a purely horizontal towing load (bite at same height as hips, in other words). Here we have our classic 45,45,90 triangle, and you can see the horizontal component would be the same length as the vertical--meaning eight tons pulling force. However, if you angle the side-force vector down in front (bite lower than hips) that raises the point of intersection with the leg component, and results in more pulling force. With a ceratops on its side (the most likely tow position, I would think) and the rex biting the frill two feet off the ground, that gives a bite to hip angle of 13 degrees, raising the tow force to 10 tons. Short of getting wedged between rocks or trees, this would almost certainly have been enough to get a four or five ton ceratops moving. Even at the more modest figure of 60 degrees leg angle, 20 degrees bite to hip angle (this angle increased because the hips went up but the bite height stayed the same) that still gives you about 6.3 tons tow force. If you want to measure how much towing loads up the legs, just measure the length of the leg component. In the first example, (45 deg. foot to hip, 13 degrees bite to hip) that would have been almost 15 tons, and in the second example (60/20) that would have been nearly 12 tons. If you will remember, in my last post, I showed that the rex hip would have had to have been overrated by more than 100% to carry a Big Happy Meal, so these leg loads would probably have been well within spec. (Yes, that's right. Dragging with ten tons force would have put LESS load on the hips than eating two tons.) Other considerations. The highest drag is in getting a body moving. Once moving, drag drops. Wet vegetation would help reduce drag. Blood would really help reduce drag. Also, if you were going to tow a ceratops, the top of the frill would probably have been the place to clamp on. (Assuming a rex could turn it's head sideways like that.) I heard it suggested that the rex could have been moving the corpse to conceal it, which doesn't strike me as very likely. I think I missed a couple of episodes of this thread, though. Did anyone think to suggest this rex could have been trying to drag this body back to a den/nest/whatever to feed little rexlings? I'm still skeptical of any post mortem scenario, just because I think when you combine a rex and a dead ceratops, you get shredded ceratops, and I gather that wasn't the case here. But thanks to Jack pointing out my woolly thinking, I see now that I can't invoke my previous argument against the relocation scenario. If anyone sees where I've put another foot in it while trying to extricate this one, don't just stand there, grab a shoehorn and do something! Nick PS Something I was wondering about. How precisely do rex teeth mate up? Close enough to remove meat purely by cutting, or would the rex have had to tear loose the sinews that pass between the teeth? I used to think the rex would bite most of the way through and then lift to tear hunks of meat out, but after my last post, I realized it would not have had enough lift capacity. If the teeth don't mate well enough for a clean cut, would shaking the head have been sufficient to tear the meat out? If not, I was thinking the rex might have been able to use it's prodigious towing ability to pull hunks of meat loose, since it apparently had several tons capacity to play with. Just a thought. PPS If any of you math masochists out there want the formulaic version for figuring tow loads, I'll post that.

**Follow-Ups**:**Re: Rex Towing Capacity (Aaargh!)***From:*Richard W Travsky <rtravsky@uwyo.edu>

**Re: Rex Towing Capacity (Aaargh!)***From:*Jack <jconrad@lib.drury.edu>

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