# Archery Calculator

### Input the necessary information and learn kinetic energy, velocity, and momentum!

Arrow Kinetic Energy = {{ calcKineticEnergy }} ft-lbs

Arrow Velocity = {{ calcVelocity }} ft/sec

Arrow Momentum = {{ calcMomentum }} slug-ft/sec

## FOC Calculator

### Input the necessary information and learn the Foward of Center balance point

Arrow FOC = {{ calcFoc }}%

``` new Vue({ el: "#archery-calculator", data() { return { IBO:'', drawLength:'', drawWeight:'', arrowWeight:'', additionalWeight:'', arrowLength:'', distanceFromNock:'' } }, computed: { calcVelocity: function(e){ let ibo = this.IBO; let dL = this.drawLength; let dW = this.drawWeight; let aW = this.arrowWeight; let adW = this.additionalWeight; let result = ibo + (dL - 30) * 10 - adW / 3 + Math.min(0,-(aW - (5*dW))/ 3); let truncated = Math.round(result); if (truncated > 0){ return truncated; }else{ return 0; } }, calcKineticEnergy: function(){ let ibo = this.IBO; let dL = this.drawLength; let dW = this.drawWeight; let aW = this.arrowWeight; let adW = this.additionalWeight; let s = ibo + (dL - 30) * 10 - adW / 3 + Math.min(0,-(aW - (5*dW))/ 3); let result = (aW*(s**2))/450800; let truncated = Math.round(result); return truncated; }, calcMomentum: function(){ let ibo = this.IBO; let dL = this.drawLength; let dW = this.drawWeight; let aW = this.arrowWeight; let adW = this.additionalWeight; let velocity = ibo + (dL - 30) * 10 - adW / 3 + Math.min(0,-(aW - (5*dW))/ 3); let momentum = (aW * velocity)/225400; let truncated = momentum.toFixed(2); return truncated; }, calcFoc: function(){ let aL = this.arrowLength; let dN = this.distanceFromNock; let result = ((100 * (dN-(aL/2)))/aL); if (result > 0) { return result.toFixed(1); } else{ return 0; } } } }); ```

# Why an Archery Calculator is Useful and How to Take Advantage of It

Do you know how much your arrows weigh? Do you understand how arrow weight affects your archery performance in the field or at the range? That's somewhat of a loaded question, right?

The arrow weight is one of the determining factors involved with the physics of your shot. Arrow weights determine speed, drop rate, and penetration at the target.

Shooting with the wrong arrow weight for your bow damages your equipment, and you could experience an injury. That's why bow manufacturers design models for shooting specific arrow weights.

So, how do you calculate the arrow weight and settle on the right arrow for your archery? This post unpacks everything you need to know about calculating arrow weights, and we'll give you a simple solution using our archery calculator.

## How Fast Do Arrows Travel?

Let's look at a practical example of understanding arrow speed using an IBO 300 bow. The exercise aims to understand what happens to the arrow speed when you increase arrow weight and draw length on the bow.

First, choose the draw length; let's settle on 32-inches. Next, decide on your arrow weight and draw weight. For instance, let's say you keep the peak draw weight at 70-lbs, but increase arrow weight to 400-grains.

Note any additional weight on the bowstring and write it down to record your findings for later use. For our example, we'll assume the extra weight works out to 5-grains.

Next, input all the variables into your 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

After completing your calculation, you'll end up with the result of the arrow traveling at 301.67 feet per second.

## Understanding the Concept of Bow and Arrow Kinetic Energy

The total kinetic energy output of the bow equates to its measurable power. This calculation depends on two variables, the speed and the mass of the arrow.

You can calculate the kinetic energy in the arrow using the following formula.

KE=(mv²)/450,240

In this equation, m = the arrows mass in grains, and v = the velocity in fps.

If we look at the standard field setup of a bow shooting a 400-grain arrow at 250 fps, the kinetic energy involved in the shot will work out to the following.

• KE = (mv²) /450,240
• KE =[ (400)(250²)] /450,240
• KE = 25,000,000 /450,240
• KE = 55.53 ft-lbs.

So, what does kinetic energy all add up to when it comes to shooting performance in the field?

Kinetic Energy

Target Size

Under 25 ft-lbs.

Small game (groundhog, rabbits)

25 - 41 ft-lbs.

Mid-sized game (antelope, deer)

42 - 65 ft-lbs.

Large game (bear, elk, wild boar)

Over 65 ft-lbs.

Big Five and safari game (Musk ox, cape buffalo)

According to professional North American hunters, shots using 55-ft/p-lbs. is enough to handle the largest game.

It's important to note that bow hunting is a traditional and immersive sports experience. You'll find that your results at the range differ in the real-world hunting environment due to the elements of change in the field.

Regardless of the time and effort you spend calculating, evaluating, and refining the numbers in your preseason; there's no guarantee it will work out like that in the field. Complex variables that arise on the hunt test the limit of any mathematical model.

When you're making the shot, you also need to consider the punching power of the arrowhead and its need to penetrate tough hide, sinew, muscle, and even bone. This dynamic occurs in an uncontrolled outdoor environment, and there is no guessing what could happen when you take the shot.

It's possible to get unlucky and blow the shot, and it's also possible for lady luck to land on your si8de when you think you're making a mistake. The dynamic of the great outdoors plays its role in the fate of your shot in many cases. However, that's all part of the sport we love so much.

With high-quality equipment, excellent technique, and smart hunt planning, you can tip the scales in your favor, maximizing the chances of success with your hunt.

## What Is Arrow FOC and How Does It Impact Arrow Flight?

In archery, FOC stands for "front-of-center." FOC involves the total weight percentage found in the front half of the arrow. The more the weight is in the front of the arrow, the more forward the arrow's center-of-balance.

The FOC balance of the arrow affects the arc of the arrow trajectory. Ideal FOC is critical for those target shooters competition in long-range contests using Olympic-style rules, like FITA Archery events. While FOC is less relevant during short-range shots, it's essential to long-range archery or when shooting low-poundage equipment.

Archery experts generally accept a high FOC offers you better stability in flight, but the drop-off sheds the trajectory quicker, making it suitable for close-range hunting scenarios. An arrow featuring low FOC holds its flight path but loses efficiency and accuracy on the flight path.

According to Easton, arrows featuring a 10 to -15% FOC are the best choice for hunting and distance shooting.

## Steps for Calculating Your Arrow FOC

To determine the arrows FOC, make sure you have a complete mock-up of all the components you'll be using, such as the points or broadheads, inserts, vanes, nock, and others. After you complete the arrow setup, do the following.

1. Divide the total arrow length in half.
2. Find the balance point by resting the arrow on your finger until it balances level.
3. Mark the point and measure the distance of the balance point from the front.
4. Subtract the figure from the first calculation and multiply the result by 100.
5. Divide the result by the length of the arrow to get the FOC value.

If you notice the arrows FOC differs significantly from the recommended 10 to 15% range, consider adding or removing weight.

### How to Manipulate Arrow FOC.

When you add weight to the front or rear of the arrow, it changes the FOC and the arrow's balance. Using heavier vanes can reduce FOC while using feathers for vanes improves FOC.

## Unpacking Bow Speed IBO Specifications

Most of the professional bow models from top manufacturers utilize the IBO (International Bowhunting Organization) specifications. This spec determines arrow speed under the following parameters.

• Draw lengths equal to 30-inches.
• Draw weights equal to 70-lbs.
• Arrow weights are limited to 350-grains.

Deviating from these parameters means the arrow speed won't meet IBO specifications. However, it's important to note that most archers deviate from these guidelines, and they choose a setup that works for their individual style.

This situation is where it comes in handy to know how to do your calculations yourself. This approach lets you understand arrow performance in a variety of environments and bow settings.

## Principles for Effective Archery Calculations

You'll need to adjust the arrow speed from the IBO specification using the following guidelines.

• For every 1-inch of draw under 30-inches, subtract 10 ft per second from your IBO value.
• For every 1-inch of draw above 30-inches, add 10 feet per second to your IBO value.
• For every 3- grains of arrow weight above the draw weight, multiplied by 5, subtract one foot per second from your IBO value.
• For every 3-grains of extra weight on your bowstring, subtract one foot per second from your IBO value.

All of these rules fit into a common equation.

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

With this equation, you have the following values.

• v = Arrow speed in ft/s.
• IBO = Arrow speed to the IBO specifications in ft per second.
• L = Draw length in inches.
• W = Additional bow string weight in grains.
• A = Arrow weight in grains.
• D = Draw weight in-lbs.

You can also calculate the momentum and kinetic energy of the arrow using the following calculations.

• Momentum = A * v
• kinetic energy = A *v^2 / 2

## Why an Archery Calculator is Useful and How to Take Advantage of It

So, after your math class, you have everything you need to calculate your arrow speed and understand how the arrow variables play into your shooting experience.

However, who has the time and patience for calculations these days? Sure, we get the importance of understanding the process and its role in archery, we still believe that everyone should understand how to calculate arrow speed manually successfully.

However, we live in the tech era, and there will always be an app for that. Why go to the hassle of doing your calculations when you can have an algorithm do it for you accurately?

With our archery calculator, you get accurate results instantly and a better shooting experience in the field or at the range.