arrow speeding after release

What Is The Arrow’s Velocity As It Leaves The Bow?

What Is The Arrow’s Velocity As It Leaves The Bow? Well, that depends on a number of factors: Gravity, arrow weight and type, bow efficiency, and more.

In general, The majority of recurve bows in the 45-pound range with 28-inch draws will discharge an arrow at roughly 200 feet per second.

The speed of the arrow is determined by a number of elements, including the bow’s material, the bowstring’s material, the draw weight of the bow, the draw length of the bow, and the weight of the arrow. The more the weight of the limbs and the more they are drawn, the faster they will move. Here’s how you can measure the draw weight and draw length of your bow.

The majority of Olympic-style recurve bows in the 45-pound range with 28-inch draws will discharge an arrow at roughly 200 feet per second. When the bow is released, it should exert all of its force on the arrow until the string returns to its original position. With the string, the arrow would be moved 26 inches from its sketched position.

Then 147 Joules of energy should be applied to the arrow. We can ignore gravity if we assume the arrow is shot horizontally, thus all of that energy will flow into the arrow and become kinetic energy. (1)

Arrow Speed

Arrows come in a variety of weights, which are measured in grains. This is the entire weight of the finished arrow, including the insert, shaft, vanes, and nock, and it can range from lightweight (350 to 400 grains) to standard weight (400 to 445 grains) to heavyweight (500 to 600 grains) (445 to 750 grains).

Even when shooting a light arrow, most modern crossbows send shafts with significantly more kinetic energy than is required to accomplish a good shot. The ballistic advantages of heavier arrows are explained above, but there is another advantage. Energy is left in the bow assembly after the crossbow shoots an arrow, which is absorbed and subsequently dispersed by the bow’s parts. (2)

Here is the chart for Arrow speed and kinetic energy:

Arrow Speed and Kinetic Energy by Arrow Weight

ArrowModel AModel BModel C
Draw Weight185 lbs180 lbs175 lbs
Arrow WeightFPS, KEFPS, KEFPS, KE
370 grains364, 109345, 98336, 93
425 grains345, 113327, 101322, 98
435 grains342, 113324, 102318, 98
545 grains312, 117296,  106292, 103

Formula

The IBO-specified arrow speed should be modified according to the following guidelines:

Subtract 10 ft/s from the IBO value for each inch of draw length less than 30″.

Add 10 ft/s to the IBO value for every inch of draw length exceeding 30″.

Subtract 1 ft/s from the IBO number for every 3 grains of total arrow weight overdraw weight multiplied by 5.

Subtract 1 ft/s from the IBO figure for every 3 grains of additional weight on the bowstring.

All of these rules can be summed up as follows:

v = IBO + (L – 30) * 10 – W / 3 + min (0, -(A – 5D)/3)

Where:

v represents the actual arrow speed in feet per second.

IBO represents the arrow speed according to the IBO specification in feet per second.

 L represents the draw length in inches.

W represents the additional weight on the bowstring in grains.

A represents the arrow weight in grains.

D represents the draw weight in pounds.

Consider the following scenario: you’re examining the IBO 300 bow. When you increase both the draw length and the arrow weight, you want to know how fast the arrow is moving.

Choose the length of the draw. Let’s suppose it’s the same as 32″.

Make a decision on the draw and arrow weights. Assume you keep the standard peak draw weight of 70 lbs but use 400-grain arrows.

If there is any extra weight on the bowstring, make a note of it. Assume that its weight equals 5 grains.

Put all of these numbers into the arrow speed formula:

v = IBO + (L – 30) * 10 – W / 3 + min (0, -(A – 5D)/3)

v = 300 + (32 – 30) * 10 – 5 / 3 + min (0, -(400 – 5*70)/3)

v = 300 + 2 * 10 – 1.66 + min (0, -(400 – 350)/3)

v = 300 + 20 – 1.66 + min (0, -50/3)

v = 318.33 – 16.67

v = 301.67 ft/s

Many bowhunters are baffled by the complexities of bow velocity. They see a bow’s IBO speed rating and assume that if they buy that bow, they’ll obtain that raw arrow speed, if not a little faster. But that doesn’t happen very often.

The common method for calculating a bow’s draw arrow speed is complicated and specific. The IBO system calls for a 5 grain per pound draw weight bow and arrow. The ATA rating, which uses a 30-inch draw length, 70-pound draw weight, and 350-grain arrow, is another popular speed rating.






References
(1) kinetic energy – https://www.britannica.com/science/kinetic-energy
(2) Energy – https://www.eia.gov/energyexplained/what-is-energy/

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