Force/draw curve

[DC]

Laying in bed the other night and this came to me. If I hang a pulley on a tree and put 40# on a rope, stick the other end through the pulley and tie it to a scale. Just turning vertical motion to horizontal. Now pull the scale until the weight clears the ground. Now start an F/D graph as I pull it 20". I'm going to get a graph that starts at 40# and ends at 40#. Heck of a curve, roughly twice as much stored energy as any other graph I've seen. If I nock on arrow in the rope and let go it's going to go about ten feet. The F/D graph is misleading is it not? This contraption is powered by gravity and gravity ain't that fast. So I'm thinking that a a lot of stored energy ain't worth a pinch unless you can somehow factor in the speed of the return but that depends on the stored energy. It took me quite a while to fall asleep Can someone point out the flaw in my thinking?

[gfugal]

Great thought experiment!!

Acceleration of return is a thing that is not if ever brought up, when clearly it's so important. I'm guessing wood, in general, has a similar return rate, so it's mostly ignored, but it's possible some species are more springy than others? However, I think you can mostly address it with efficiency. That gravity shot is not very efficient at all. How hard is that weight going to hit the ground even when you put an arrow on the end? I'm guessing pretty dang hard. That means it still has a lot of that energy and it wasn't transferred well to the arrow. talk about hand shock. Could you imagine hand shock equivalent of 40 lbs hitting your hand after being dropped from 2 feet?

[DC]

OK this has been worthwhile. I now understand a little better what you guys mean when you talk of efficiency.

[Badger]

  Springiness in not ever mentioned because it is irrelevant. You have stored energy, virtual mass and hysteresis. Hysteresis is what you are referring to as springiness. The rest of the losses are in vibration and distortion of the limbs and have no relation to hysteresis. If you can successfully tiller a bow with no set visible or otherwise it will have extremely low hysteresis and be more springy.

[DC]

I think the only hysteresis in my example would be the friction in the pulley. Not much. If we re-engineer my example and introduce some leverage we more or less have a trebuchet. They work pretty well. It seems to me that introducing speed into this increases the transfer of energy. The harder it has to work the more efficient it is.

[Badger]

  On your pulley it would have 800" pounds of energy. The only loss it would have would be a very small amount of air resistance. Now once you start converting that into useful forms of work you start loosing efficiency as it would require some structure in place to convert the energy.

[Bayou Ben]

What is storing energy in your example DC?
If there's no device such as a limb to store the accumulated work done then you don't have a force draw curve.  You have one point on the graph.  Or am I missing something?

[gfugal]

  Springiness in not ever mentioned because it is irrelevant. You have stored energy, virtual mass and hysteresis. Hysteresis is what you are referring to as springiness. The rest of the losses are in vibration and distortion of the limbs and have no relation to hysteresis. If you can successfully tiller a bow with no set visible or otherwise it will have extremely low hysteresis and be more springy.

I used springiness for lack of a better word which I think would make sense to more people than hysteresis. You can reduce hysteresis by minimizing set, but regardless of whether you get set or not there is always going to be some hysteresis. I'm just wondering if some materials have less of it than others.

[gfugal]

What is storing energy in your example DC?
If there's no device such as a limb to store the accumulated work done then you don't have a force draw curve.  You have one point on the graph.  Or am I missing something?

Potential energy is stored energy. So in bows that potential energy is stored in the limbs as they want to return to their unbraced profile. In DC's example, the energy is stored in the weight's position being suspended above the ground.

[DC]

What is storing energy in your example DC?
If there's no device such as a limb to store the accumulated work done then you don't have a force draw curve.  You have one point on the graph.  Or am I missing something?

Lifting the weight off the ground and making a mark every inch.

[Bayou Ben]

Yep I got it now.  I guess what Badger is saying is the big question. How do you move that PE into work to propel the arrow?

[Springbuck]

Now, imagine dropping that weight onto the short end of a lever over a fulcrum, say ten feet long with 9 feet on one side and one foot under your weight.  Let's make it a 1" diameter bamboo pole, and let's set a ball bearing the weight of an arrow on the long end.  Now what happens?

  The bearing may rocket away, but most of the stored energy still went into the floor.

[GlisGlis]

I may be completly wrong but it seems to me that when you pull a 40# bow at the right drawlenght the force along the string (tip to tip lengthwise) is much more than 40#

[DC]

If you make a string with a scale in it you can watch this. I did. A 40# bow has about 45# of string tension at brace. The lower the brace, the higher the tension. As you draw the bow the string tension goes down . It was a while ago I did this but I think the string tension was always more than the draw weight. It was very strange to pull the bow and watch the scale go down the more you pulled.

[Bayou Ben]

Thanks DC, now I have a couple hours of thinking to make that string tension thing make sense to me...lol