Crossbow Physics: Calculating Spring Constant, Tension Force & Power

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Discussion Overview

The discussion revolves around calculating the physics parameters of crossbows, specifically focusing on the spring constant, tension force, and power associated with the launch of arrows. Participants explore the relationships between potential energy, kinetic energy, and the mechanics of crossbow operation, including the effects of spring linearity and energy transfer timing.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Peter introduces a project to measure crossbow parameters using arrow velocity and provides specific data for calculations, including mass, tension distance, and formulas for spring constant and tension force.
  • Some participants suggest that energy conservation is a useful approach for calculating arrow velocity, noting that the force is not constant during acceleration.
  • Concerns are raised about the assumption of linearity in the spring's behavior, with some participants recommending that Peter check the linearity before proceeding with calculations.
  • There is a discussion about the implications of non-linear spring behavior on the potential energy expression and the need for integration to accurately model the system.
  • Participants share insights on the differences between linear and non-linear springs, with references to graphs illustrating the draw curve of different types of bows.
  • Peter expresses uncertainty about how to calculate the time required to transfer energy to kinetic energy, seeking further recommendations from the group.
  • Some participants discuss the potential complexities introduced by the design of the bows and the nature of the spring mechanism used.
  • There is a question raised about the interpretation of a graph shared in the discussion, indicating some confusion regarding the relationship between force and draw distance for conventional bows.

Areas of Agreement / Disagreement

Participants generally agree on the importance of checking the linearity of the spring and the need for accurate modeling of the energy transfer process. However, there remains disagreement and uncertainty regarding the implications of non-linearity and the interpretation of related graphs.

Contextual Notes

Limitations include the assumption of spring linearity, potential friction losses, and the need for integration in cases of non-linear behavior. The discussion also highlights the complexity of the crossbow design, which may affect the calculations.

Who May Find This Useful

Individuals interested in the physics of archery, mechanics of crossbows, and those involved in experimental physics projects may find this discussion relevant.

  • #31
OK - we'll start again . Please post a good drawing of the actual set up . Include detailed dimensions and materials information for the metal bar and for the elastic string .
 
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  • #32
This is the set-up:

upload_2017-4-9_10-48-2.png


I can measure the velocity of the departing arrow. The mass of the rubberband spring is unknown and not practical to measure.

I would be interested to use the velocity and the other known parameters to calculate bow characteristics including the power of the bow.

Let me know if you need more information!
 

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  • #33
What are the cross sectional shape and dimensions of the rubber band and what material is it made from ?

Alternatively (or in addition) - what extensions of the actual rubber band do you get under different applied loads ?
 
  • #34
The rubberband has a round shape (rod shape) with a diameter of about 5 mm. I will post a picture of the actual bow later today.

I have no equipment to measure extensions under different loads, so I don't have or can easily collect that information.
 
  • #35
pevi70 said:
I will post a picture of the actual bow later today

Yes please - that would be very helpful .
 
  • #36
Despite the picture, quite some assumptions need to made: no recoil for example.
If you would assume that the propulsion is coming only from a mass less rubber spring, no friction exists, how would you calculate the time it would take for the arrow to cross the 17.5 cm (knowing the final speed)?

How could I approach that?

Thanks for your thoughts!
 
  • #37
pevi70 said:
I have no equipment to measure extensions under different loads, so I don't have or can easily collect that information.
Extension of the rubber band can be measured easily enough with a ruler. If you don't have a dynamometer on hand, you can measure draw force the way it was traditionally measured - hang the crossbow on a wall, and attach weights of known mass to the spring, measuring the distance the nocking point moves for each weight (hence the traditional nomenclature for bow power - 'draw weight'), as well as the associated extension of the rubber band.
Different crossbows are then ranked by their draw weight at full draw.
 
  • #38
Thats simply not practical. You need a special lever to lock the spring. I can measure the speed of the arrow.

I would really appreciate it if someone could help me how to calculate the time needed to propel the arrow by the spring in an idealized environment.
 
  • #39
?
Why would you need to lock the string? Get a bottle, fill it with sand, weigh it, then attach it to the string and measure how much it stretches. Then change the bottle for a different weight or add more bottles and repeat.
 
  • #40
These bows are so strong, you need a special lever to charge the spring.
 
  • #41
If you do it by hand, sure. But here you're just hanging weights on the string. You can hang as much as it takes. I really don't see the problem here.
I really don't have any experience with stretching strings, but if it's anything like traditional bows in efficiency, then you'll need something like 50-70 kg at full draw for 60m/s bolt (which you don't need, since we just want to find out how the string extension vs draw weight looks like - the first few cm of draw should suffice).
 
  • #42
Here is a picture of the bow:
(The width of the wooden part of the bow is 4 cm)

Crossbow.jpg
CrossbowZoom.jpg
 
  • #43
Since you can measure v (velocity at the arrow separation); and, for an object accelerating from 0 to v, s= 1/2vt, and with s and v then you can determine t (time of acceleration) and subsequently the acceleration a. If of any benefit, from that using F = ma you can determine the average effective bow force. (if, as you specified, you ignore friction and recoil.)

Edit: I just saw thr bow picture and are you sure there is no flexing of the crossbar? If there is as strong a pull force as you state, it is hard for me not to expect flexing in that component.
 
  • #44
I think s=1/2vt only applies if the acceleration is constant.
 
  • #45
What this will give you is the average acceleration for the entire travel, not the profile of the acceleration. For for a given succession of values regardless of linearity there exists an average value.
 
  • #46
OK, I thought it didnt apply. Thats great, thanks a million!
 
  • #47
bow spring v3.png
I estimated the dimensions but they won't be far out . 150 N on each arrow .
 
  • #48
Thanks Nidum, what is it?
Do you agree with JBA?
 
  • #49
FEA deflection estimate for the bow .

If deflection had turned out to be very small then it would have confirmed what you have said about bow being just a rigid bar .
 
  • #50
What does that mean?
And do you agree with JBA?
 
  • #51
Problem is that all responders - including myself - are now a bit uncertain as to what exactly we are trying to analyse .

So I'm trying to get a definite understanding of the mechanics of this cross bow . Is it the metal spring , the rubber rope or a combination of both that provides the driving force ?
 
  • #52
Do you agree with JBA?
 
  • #53
Nidum said:
So I'm trying to get a definite understanding of the mechanics of this cross bow . Is it the metal spring , the rubber rope or a combination of both that provides the driving force ?

Amen!
 

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