String angle and energy

[chasonhayes]

my understanding with my physics background is to separate the string tension from the pulling weight.
The most efficient pulling angle is always 90 degrees which gives the longest effective moment arm. Above and below that are less effective but since string tension is so low when the bow is initially drawn the inefficiency is not noticed. Until the 90 degree angle is achieved as string tension increases the moment becomes more efficient mitigating the increased force created in the string. It is only as the angle passes 90 degrees that it becomes less and less efficient and of course the string tension is also increasing so the lack of mechanical advantage becomes more apparent. Think of leverage - hold a 30lb weight straight out is much harder than holding is straight down or straight up but the force is the same. In this example the weight is the string tension, the position of your arm is the string angle, and the effort is the pulling weight.

As explained above stacking occurs when the combination of high string tension and large angle(smaller moment arm) create an exponential increase in force to draw the string back.

So a recurve that measures 35lbs pulling weight might have the same string tension as a straight bow that measures 50lbs at the same draw length. Or put another way if both bows measure the same pulling weight, the string tension and energy stored will be greater in the recurve due to a better mechanical advantage. That is why those short horn bows worked so well but no wood could handle that level of string tension.

[PatM]

That is why those short horn bows worked so well but no wood could handle that level of string tension.

 Not sure what you mean by this.  Wooden bows aren't limited by string tension.

[Allyn T]

This is from TBB4 but it doesn't explain the why. It also looks like a pretty negligible gain if two bows are close in length.

"One of the cruel realities of bow design is that shorter straight bows can’t be as fast per pound as longer straight bows, even at equal draw length. Between 35” and 60” possible performance rises roughly 1 fps per inch of bow length. Cast rises slowly from there to around 68”, then only minor improvement from there to 80”, and only then if given more elliptical tiller."

[Selfbowman]

I like it when the smart guys share.🤠

[Yooper Bowyer]

What I meant was that longer bows have fatter FD curves, which is the same as saying that they store more energy all else equal. 

Stack is the opposite of a fat F/D curve, so a bow that stacks hard at full draw will store as much energy as a longbow that draws the same weight at the same distance. 

This also depends on brace height of course, as it cuts into the total 'draw length'.

Stack happens when the string angle gets large because of changes in leverage, as indicated above.

How this translates to arrow speeds depends on several other variables.   

[Morgan]

This is from TBB4 but it doesn't explain the why. It also looks like a pretty negligible gain if two bows are close in length.

"One of the cruel realities of bow design is that shorter straight bows can’t be as fast per pound as longer straight bows, even at equal draw length. Between 35” and 60” possible performance rises roughly 1 fps per inch of bow length. Cast rises slowly from there to around 68”, then only minor improvement from there to 80”, and only then if given more elliptical tiller."

The last part of the quote from TBB goes parallel with what Bj was saying earlier about pushing forward rather than outward. There has been much discussion on proper tiller shape for a given front profile. I’m not certain if that is for longevity or performance or both but if the forward not out movement is what lends to better performance, wouldn’t an elliptical tiller always be desirable from a performance stand point?

[Selfbowman]

Ok this pic is not at 90 degrees cause I can’t my bow some for better sight on bringing the broadhead to full draw . What’s the string angle?

[Selfbowman]

Probably had 1-11/2 “ to get to full draw.

[Yooper Bowyer]

Probably between 60 and 70 degrees between the arrow and string.

[Morgan]

A good ways from 90.

[simk]

my understanding with my physics background is to separate the string tension from the pulling weight.
The most efficient pulling angle is always 90 degrees which gives the longest effective moment arm. Above and below that are less effective but since string tension is so low when the bow is initially drawn the inefficiency is not noticed. Until the 90 degree angle is achieved as string tension increases

Thank you chasonhayes for your thoughts! I think its a good idea to string tension into play. It maybe helps understanding what really happens. Altough I must say your basic assumption is very wrong: String tension definitly is highest at brace and then goes down when drawing the bow.

 

[sleek]

my understanding with my physics background is to separate the string tension from the pulling weight.
The most efficient pulling angle is always 90 degrees which gives the longest effective moment arm. Above and below that are less effective but since string tension is so low when the bow is initially drawn the inefficiency is not noticed. Until the 90 degree angle is achieved as string tension increases the moment becomes more efficient mitigating the increased force created in the string. It is only as the angle passes 90 degrees that it becomes less and less efficient and of course the string tension is also increasing so the lack of mechanical advantage becomes more apparent. Think of leverage - hold a 30lb weight straight out is much harder than holding is straight down or straight up but the force is the same. In this example the weight is the string tension, the position of your arm is the string angle, and the effort is the pulling weight.

As explained above stacking occurs when the combination of high string tension and large angle(smaller moment arm) create an exponential increase in force to draw the string back.

So a recurve that measures 35lbs pulling weight might have the same string tension as a straight bow that measures 50lbs at the same draw length. Or put another way if both bows measure the same pulling weight, the string tension and energy stored will be greater in the recurve due to a better mechanical advantage. That is why those short horn bows worked so well but no wood could handle that level of string tension.

I'm sorry but the basis of your deduction is incorrect. String tension decreases as a bow is drawn. It's at its highest at brace.

[Del the cat]

Ok this pic is not at 90 degrees cause I can’t my bow some for better sight on bringing the broadhead to full draw . What’s the string angle?

Bravo!A very good question, (which I've asked before)... is it the angle with the last 2" of limb? The last 10"? Half the limb? The point nearest the tip which flexes.
this illustrates nicely how complex the physics and geometry. Even the most extensive analysis relies on simplification.
Del.
PS. My instinct would be to draw a line from the very tip to a point about 4" or so, down from the tip and use that to measure the angle.

[BowEd]

Yes at the bows' tip is the angle that's important.

[simk]

sometimes simplificated pics help.

I made 3 drawings for you:

Situation A: String angle less than 90
Situation B: String angle 90
Situation C: String angle more than 90

As you can see, the drawforce induced from the string (vector) at 90 degrees goes 100% into the bend of the limb.

In Situation A and C its different.... this force at the tip is split into two vectors:

In Situation A its being split into one part that goes into bend and one part working somehow like a compression force to the limb (GREEN)

In Situation C its split into one part that goes into bend and another part that goes into stretch of the limb (RED)

According to my primitive understanding GREEN = GOOD and RED = BAD.

I can also understand why RED = BAD, but not fully why GREEN = GOOD