Medieval Physics - Bows & Arrows

Of the many interesting events that take place in the summer, one of my favorites are Renaissance fairs. Seeing the participants in character and costume is an entertaining tribute to the days of knights and castles. However, the combat and jousting presentations rarely do justice to their crafts. As such, I thought it would be neat to dive into some of the science behind medieval sport and combat. To start, let's take a closer look at a practice that predates recorded history: archery.

Archers (users of the bow and arrow), were a common element among most warring nations in Medieval times. Before the age of gunpowder, bows were the only weapons available to foot soldiers that could significantly extend their range of combat. Some bows (specifically longbows) had the ability to launch a deadly arrow over great distances and with great force. Between the 14th and 16th centuries, the English longbowman (seen left) was a force to be reckoned with due to the range and power of his weapon.

While there is a lot of diversity among bows and arrows, all essentially consist of three parts:

1. the bow (or bowstave) - a flexible arc shaped piece with a handle grip near the center, a notch to hold the arrow, and attachments for the string at either end. They can be made from wood, bone, metal, plastic, or carbon composite

2. the arrow - a straight projectile made of similar materials to the bow, with a pointed metal blade on the front, and fletchings (plastic fins or feathers) on the back.

3. the bowstring - a strong thread of hide, intestine, or artificial materials attached to both ends of the bow to hold it taut.

A bow and arrow works like a spring. When the archer pulls the string back (called drawing), the string puts compression and tension forces on the bow, bending it and storing elastic potential energy. When the string is released, the tension between the bow and the bowstring causes the string to move forward rapidly as the elastically deformed bow returns to its original position. The result (hopefully) is a large transfer of energy from the string to the attached arrow, turning it into a high speed projectile.

When released, there is a certain amount of force put on the back end of the arrow from the bow and the archer's fingers (or other release mechanism). This force causes the arrow's backend to wobble. The fletchings on the arrow catch the wind in order to correct this movement and help the arrow fly true. Larger fletchings will correct wobble faster, but will create slightly more wind resistance. Configuration of the fletching into different patterns (helical or offset vs. straight) can add spin to the arrow to further help dampen oscillation.

There are a number of other variances in arrow construction that can be chosen based on the preferences and shooting style of the archer. The same goes for the construction of bow, which needs to be much more fit to the user than a firearm in order to shoot well. Bow length, draw length and draw weight are the three biggest factors by which bows will vary.

Bow length is obviously important because length determines the size, which must fit to the size of the shooter and his needs. Power increases with bow size, however, a recurve style bow will generate more arrow energy than a straight bow of the same size. This is because of the curves near the limbs, which allow for greater energy storage and more efficient energy transfer. Because of this, the recurve bow was preferred in situations (such as on horseback or in wooded terrain) where extra length could affect an archer's mobility.

A related characteristic is draw length - the distance the archer pulls back the string, measured from the nock point on the bow. Bow size and the size of the archer determines draw length, which in turn affects the size and length of the arrows used. A basic method for estimating appropriate draw length is to divide the archer's arm span by 2.5. Having too much or too little draw can affect accuracy and shooting consistency.

The draw weight, which is the max resistance of the bow when being pulled back, is also very important for the archer to consider. A higher draw weight means more strength is needed to pull and hold the bowstring in tension, but it also means a more powerful shot. Yeoldarcheryshop.com provides a nice chart that correlates draw weight (DW) to archer weight:

Small child (50-70 lbs) --> 10-15 lbs DW

Child (70-100 lbs) --> 15-25 lbs DW

Most women, boys from (100-130 lbs) --> 30-40 lbs DW

Women above average strength; youth boys (130-150 lbs) --> 40-50 lbs DW

Most men (150-180 lbs) --> 55-65 lbs DW

Muscular young men and larger men (>180 lbs) --> 60-70 lbs DW

Compare these numbers to back in Medieval times, when estimates say the draw weight of the longbowmen ranged anywhere from 80 to 180 pounds! Pretty unbelievable.

Today, archery and bowhunting has advanced to the use of the compound bow, utilizing pulleys and wheels to generate more power and accuracy with less exertion. Unlike recurve and longbows, which have a linear relationship of draw weight to draw length, compound bows have a parabolic relationship, because the levering system of these bows allows for a lower draw weight when extended past a certain draw length.

Despite such advances in technology, the art of the recurve bow has been preserved in the Olympics, keeping alive a fascinating skill and practice that has been around through the ages.

Sources:

The Mechanics of Arrow Flight

Bow Sizing and Adjustment Guide