彈弓 台灣 BUSHCRAFT TAIWAN

德國Melchior Menzel先生關於彈弓性能的物理性質說明,原文附翻譯, 部分物理計算程式難以貼出,故略.

Power

a small theoretical  approach to understanding

and improving slingshot power

2006, by Melchior Menzel

威力

一個小理論的角度來理解
並提高彈弓威力

2006年，門澤爾梅爾基奧爾

Attention: The following information is based on nothing but my physics knowledge. The values are only of theoretical interest, as important facts like air drag or the power conversion to heat inside the bands are ignored. The theoretical values fit with the real data known to me surprisingly well, though.

注意：下面的信息是基於我的物理知識。數據值僅為理論的，像重要的空氣阻力或皮筋內的熱源轉換是被忽略的。雖然，理論值是很符合我所知的實際數據。

Pre-thoughts:

When the shooter releases the bands of a slingshot, the stored energy is used to accelerate bands, pouch and projectile. The way of acceleration is the shooter’s pull length minus the length of the bands.  During the forward motion, the stored energy and therefore the pull gets less until it is zero. In average, half of the pull accelerates the projectile.

當前的想法：

當射手釋放彈弓皮筋，被儲存的能量是用於加速皮筋，皮兜和彈丸。加速度的方式是射手的拉距長度減去的皮筋的長度。在向前運動期間，所儲存的能量，和拉力因此變少，直到變零。平均來說，一半的拉力是加速彈丸。

Shooting the slingshot without a projectile accelerates the band assembly to a maximum speed. The slingshot will never be able to shoot any projectile faster than this maximum velocity.

射擊彈弓不帶彈丸可讓皮筋達到的最高速度。彈弓將無法射擊彈丸超過這個最大速度。

The weight of projectile and pouch slows down the shot. The pouch end of the bands gets accelerated over the whole length, while the end at the frame doesn’t move at all. In average, half of the bands weight is accelerated

Using normal bands, doubling the pull force of the bands is only possible by doubling the weight of the bands, too. Tapered bands have more of their mass on the prong side, so less than half of their mass is accelerated. That’s why they shoot faster.

彈丸和皮兜的重量減慢飛行速度。皮兜端得到整個皮筋長度的加速，但在弓叉端是不會移動的。平均來說，皮筋一半的重量是被加速的。
使用一般的皮筋，增加皮筋的拉力一倍,皮筋的重量也可能增加一倍的。錐形皮筋，它們有更多的質量在弓叉端，所以它們有少於一半的質量來加速。這就是為什麼它們的彈丸飛得更快。

Formulas

F            = pull Force in Newton

v        =velocity

    = mass of pouch

        = mass of bands

= mass of projectile

      = complete mass to be accelerated

a            = acceleration

E            = Energy

It is , so

The pull force of the bands decreases until it is zero when the pouch has traveled the full pull length. In average, half of the force accelerates the projectile. Note that this is only an approximation, rubber does not follow Hooke’s law like a spring does. We get

皮筋的拉力減小，直至為零時，皮兜已經走過滿拉長度。平均而言，一半的力量加速彈丸。請注意，這只是一個近似值，橡膠不遵守胡克定律如彈簧一樣。我們得到

Let’s assume that projectile and pouch weight are or close to zero. This means.

假設彈丸和皮兜重量是或接近於零。這意味著

Previously, we said that doubled Power (F) means doubled bands mass (m_bands). With that in mind, the upper formula proves that a is always the same, no matter how strong the power bands are.

The acceleration – and therefore speed – of a very lightweight projectile is the same with strong and weak bands. In other words, using light projectiles is a waste of energy with powerful slingshots

先前，我們說雙倍威力（F）代表收雙皮筋質量（mbands）。考慮到這一點，上面的公式證明，a始終是相同的，無論是多麼強大的力量的皮筋。
一個非常輕量彈丸的加速 - 速度 - 用強和弱的皮筋是相同的。換句話說，使用輕彈丸在強力彈弓上是一種功率浪費。

Let’s continue. The velocity is  and , so

The energy of the projectile is

Now, we have three relevant formulas.

1)

2)

3)

With these, it is easy to calculate the theoretical speed of a any setup.

Examples:

Let’s take a setup with 70 cm, 10 grams band weight, a pouch weight of 2 grams and 20 pound pull. These values represent a slightly over-average sized shooter using common heavy pull bands.

F=20 pounds = 100 N

m= 10g + 2* 2g + 2*Projectile mass

s = 0.7 m

The weight of a steel sphere with diameter d is

Lets shoot a 1/4”, a 5/16”, a 3/8” and a 1/2”steel ball :

It is clearly visible that a lightweight projectile has much less energy than a heavier one.

這顯然一個輕量的彈丸的動能比一個較重的少得多。

Some other stuff:

一些其他的東西：

-a lightweight pouch considerably increases speed with light bands & projectile, but loses of importance with very heavy bands.

- the only way to increase the speed of light projectiles is to increase the pull length, by means of fork extension, pulley system or bands that stretch better

-tapered bands really work, and increase the speed of lighter projectiles

-heavy bands need heavy ammo

-一個輕量的皮兜大大增加輕量皮筋與彈丸速度，但搭配非常沉重的皮筋便失去重要性。
- 只有增加皮筋拉距，才能提高輕量彈丸速度，利用弓叉延伸,滑輪系統或伸展

  更好的皮筋，
-錐形皮筋真有功用，能讓輕量彈丸速度增加
-重皮筋需要重量彈丸

The following graphs are based on the formulas.

Warning: This is THEORY! The wonderful field where people can produce a lot smart-looking graphs which don’t really represent reality. Just some real facts: An ordinary slingshot propels a ½” steel ball at about 130-170 fps. A very powerful hunting slingshot with extended forks and flat bands get a 290 grain ball on 220 fps. The graphs are there to show you trends (I.e, to show you that you should be shooting heavy ammo with low-powered light bands at a high draw length to achieve good results)