Bow Mechanics 2: The Return of the String

So there you are at full draw, all that stored energy literally at your fingertips (unless you’re using a thumb draw); all that’s left is to let fly. Let’s take a look at the mechanics of what happens when you release the string. As before, I shall simplify some elements of the discussion, removing some complications such as energy lost to internal friction, heat and sound. Some of what I write will therefore not be technically accurate, but the principles are sound.

What happens on releasing the string is that the stored energy drives the limbs forward until they return to brace height, at which point the string snaps taut. String and limbs suddenly stop moving but the arrow keeps going at the same speed. Factors such as the elasticity of the string may complicate this picture slightly but I shall address that in a later post. For now we will assume that at the moment the bow reaches brace height the arrow flies off at the same speed as the string was moving a moment earlier.

Once we understand this point about the way an arrow leaves the string we are in a position to understand that if we want fast arrow speed then we need fast string speed. That follows from fast limb speed. The question is therefore how to get fast limb speed.

    Dry Fire Speed

Every archer dreads the moment some non-archer asks to try pulling their bow. “OK, but don’t let go of the string!”. Lesson 1 of archery: do not dry fire your bow. Why? Put simply, if you dry fire your bow then the energy stored in the limbs has nowhere to go. It stays in the limbs, which are not built to withstand the shock.

There is one thing to know about dry firing, apart from “don’t”: it is the fastest speed at which your limbs will move. A bow drawn and released will shoot at dry fire speed (which varies with draw length for a given bow) unless it is slowed by the mass of the arrow.

    What Determines Dry Fire Speed?

A bow’s dry fire speed is determined by the bow’s construction and the amount of energy stored in it. Energy storage was covered in my last post and I shall not go over it again here.

Bow construction also has a great effect on stored energy but in addition to this it affects the dry fire speed of the limbs for a given amount of stored energy. The main factor I shall examine here is mass. Other factors have an effect but mass is the most important one.

    Limb Mass

Sir Isaac Newton showed that Force = mass x acceleration. It follows that acceleration = force/mass. In other words, for a given amount of stored energy you will get higher dry fire speed from lighter limbs than you will from heavy limbs.

The placement of the mass is also important. The bow limb can be likened to a lever. Mass at the end of the limbs requires more energy to move than mass near the handle. Studies reported in the Traditional Bowyer’s Bible show that adding 1oz to the grip section did not slow the limbs at all, whereas adding 1oz to each limb tip slowed the bow by around 7 feet per second (fps). This is roughly equivalent to shooting an otherwise identical bow that is 7lbs lighter in terms of draw weight.

Many horsebows have siyahs: rigid recurved tips. These increase stored energy (by raising early draw weight and removing stack) but if they are too massive then they will slow limb speed. We will see below that slow limb speed combined with high energy requires a heavy arrow to avoid excessive handshock. This is because of kinetic energy.

    Kinetic Energy

Kinetic energy is the term used for the energy related to movement. Its equation is KE = 1/2mv2. In other words, kinetic energy is equal to the mass of an object multiplied by the square of its velocity (speed), all divided by 2.

When a drawn bow returns to brace height it will have no stored energy. All the energy it had stored has become kinetic energy. As the string slams taut that kinetic energy has to go somewhere. It goes into vibration of the limbs, the string, the archer (handshock) and the air (noise). There is one other place it can go: the arrow.

    The Arrow

As the string travels along the power stroke we should consider the bow and arrow as a single entity whose stored energy is being converted into kinetic energy. At the end of the power stroke there is no stored energy available – it has all become kinetic energy, shared between the bow and arrow.

At the end of the power stroke the arrow leaves the string at the final speed of the string. Since the arrow has a known mass we could calculate its kinetic energy. Without needing to do this, however, we can already see that at a given speed the arrow will have more kinetic energy if it is heavier.

We have now gone from having a total kinetic energy for the bow and arrow to having an arrow with kinetic energy and a bow that has stopped moving and therefore has no kinetic energy. Nor does it have stored energy. Any kinetic energy that has not gone into the arrow becomes vibration.

    Vibration

There will always be some vibration after the arrow flies off. The string and limbs will vibrate. This is not a problem if it is kept to a relatively low level. Nor is the noise of the string twanging, which is just the vibration going into the air.

If too much energy is left in the limbs then they vibrate too much and you feel it as handshock. In extreme cases the bow can be damaged or destroyed. This is why you should not dry-fire you bow: all the stored energy ends up as vibration.

To hunters and warriors the kinetic energy of the arrow is important: it plays a major role in determining the penetration of the arrow into the target. For a sportsman trying to obtain fast arrows the kinetic energy of the arrow is of less importance, save for this basic fact: arrows that are too heavy will slow the string too much and therefore travel too slowly. Arrows that are too light will not absorb enough energy from the bow, leaving too much energy in the limbs, which will vibrate the bow and your arm.

    What Does All This Mean?

There is a balance to be drawn when selecting your bow. Static recurves (those with recurved limb tips that do not straighten as the bow is drawn) store more energy than equivalent straight bows or working recurves (those that straighten as the bow is drawn). If those recurved limb tips are too massive, however, then even the extra stored energy will not be sufficient to move the limbs quickly.

This is especially true at low-medium draw weights. High energy/high mass bows are good for shooting at heavy draw weights and for shooting heavy arrows because they store a lot of energy but they are not so good for producing really high arrow speeds with low draw weights and light arrows. There is a reason why bows like the big Mongol recurves and the English longbow were used at draw weights of 150+lbs. The English war arrows weighed up to 1/4lb!

The ideal compromise is probably a bow that has static or partially static recurves but whose recurves are of low mass. The best examples that I have seen (and I do not pretend to have seen all available bows) are Saluki bows made by Lukas Novotny. They are of low mass but maintain their recurves for high energy storage. The resultant arrow speed is phenomenal.

So there you are: your arrow is on its way. In my next post I shall look at the way arrows fly, examining arrow mass and spine and how to get them right for your bow.

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5 thoughts on “Bow Mechanics 2: The Return of the String

  1. Hi! I’m doing a project on physics of archery and the information you have posted are really useful! Thanks a lot! I hope there is no problem with me using your work as a resource.

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