When it comes to archery, the two most important factors in determining an arrow's penetrating ability are its kinetic energy and momentum. Kinetic energy, or the power potential of the arrow, is derived from the Greek words for motion and active work, while momentum can be thought of as the ability to put that power to use by penetrating the target. The formula for calculating the momentum of an arrow is: momentum (p) = mass (m) x velocity (v). To calculate kinetic energy, use the following formula: 1/2 Mass (Arrow Weight in grains) x Velocity squared (Arrow Speed x Arrow Speed) / 225218. The speed of an arrow is determined by factors such as the bow's IBO speed, draw weight, draw length, arrow weight, and weight on the bowstring. While kinetic energy is important for penetration, momentum is critical for hunting as it helps the arrow maintain its penetration potential.

Characteristics | Values |
---|---|

Formula for momentum | p (momentum) = m (mass) x v (velocity) |

Kinetic energy formula | Mass x Velocity-squared divided by 450,240 |

Kinetic energy definition | "Power potential" of the arrow at the target, based on its mass weight and speed |

Momentum definition | Ability to put kinetic energy to work, penetrating the target |

Factors that impact arrow speed | IBO-rated speed of your bow, bow's set draw length, bow's draw weight, arrow's total weight, any additional weight on the bowstring |

Rules of thumb for draw length and arrow weight | For every inch of draw length under 30", subtract 10 ft/s from the IBO-rated speed value. For every inch of draw length above 30", add 10 ft/s to the IBO value. |

Rules of thumb for total arrow weight and additional weight on the bowstring | For every 3 grains of total arrow weight above draw weight multiplied by 5, subtract 1 ft/s from the IBO value. For every 3 grains of additional weight on the bowstring, subtract 1 ft/s from the IBO value. |

Gravitational constant | 32.174 feet per second squared at sea level |

Arrow speed formula | IBO Speed(in fps) + (Draw Length – 30) x 10 – Additional Weight on Bowstring (in grains) / 3 + MIN(0, – (Arrow Weight(in grains) – 5 x Draw Weight in Pounds) / 3) )) |

Kinetic energy formula | 1/2 Mass (Arrow Weight in grains divided by 2) x Velocity squared (Arrow Speed x Arrow Speed (in fps from the above formula)) / 225218 |

Arrow momentum formula | Mass (Arrow Weight in grains) x Velocity (Arrow Speed (in fps)) / 225218 |

## What You'll Learn

**How to calculate momentum in archery**

When it comes to archery, there are several factors that can influence the speed of an arrow after it is shot from a bow. These factors include the IBO-rated speed of the bow, the set draw length, the draw weight, the total weight of the arrow, and any additional weight on the bowstring. Even minor adjustments to these factors can significantly impact the speed, kinetic energy, and momentum of the arrow.

Kinetic energy (KE) and momentum are crucial concepts in archery, particularly in bowhunting. Kinetic energy refers to the "power potential" of the arrow at the target, and it is derived from the Greek words "kinesis" (motion) and "energeia" (active work). Thus, kinetic energy can be understood as "through motion, do active work." The formula for calculating kinetic energy in ft./lbs. is: Mass x Velocity-squared divided by 450,240, where Mass is the total arrow weight and velocity is the arrow speed.

Momentum, on the other hand, can be defined as "mass in motion." In the context of archery, momentum is important because it determines the arrow's ability to penetrate the target effectively. The formula for calculating momentum is: Momentum (p) = Mass (m) x Velocity (v).

To calculate the kinetic energy and momentum of an arrow, you need to know two variables: the total finished arrow weight in grains and the velocity of the arrow. The arrow weight can be measured using a grain scale, while the arrow velocity can be determined by shooting the arrow through a chronograph.

It is important to find the right balance between arrow speed and weight to optimise penetration power in bowhunting. While kinetic energy favours speed, momentum favours weight. Therefore, a heavier arrow will generally provide greater momentum and deeper penetration. However, lighter arrows travelling at high velocity may have higher kinetic energy.

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**How to calculate kinetic energy in archery**

When it comes to archery, kinetic energy is important for bowhunters to understand. It is the power potential of the arrow at the target, which is based on the arrow's weight and speed. Kinetic energy is what helps drive broadheads deep and is a factor in an arrow's penetration ability. Penetration is critical in bowhunting.

Kinetic energy is a concept of physics – a way to quantify the energy that an object possesses due to motion. The formula for calculating the kinetic energy of an arrow is:

KE = (m*v^2)/450,240. The m in this formula represents mass (weight in grains), the v represents velocity (speed in feet per second), and the outcome of the formula is rated in “foot pounds” (ft. lbs.) of kinetic energy.

Kinetic energy is one of several factors that can impact how far an arrow penetrates its intended target. Kinetic energy is increased when either of the two variables (mass and velocity) are increased. However, bowhunters know that both arrow weight and arrow speed cannot be increased simultaneously when other aspects of the bow setup remain the same.

To increase kinetic energy, one can increase the draw weight or draw length. The current trend in bowhunting has been to focus on speed, but testing has shown that, if kinetic energy is the goal, then increasing mass (arrow weight) is more effective than increasing velocity (arrow speed).

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**How to balance arrow speed and weight**

When it comes to archery, there are a lot of factors that can affect your performance, and finding the right balance between arrow speed and weight is crucial. Here are some tips to help you optimise your setup:

Arrow weight plays a significant role in determining how your arrow flies. Lighter arrows tend to fly faster and create tighter groups, but they can be more challenging to tune and are more susceptible to wind drift. On the other hand, heavier arrows fly slower but resist wind better and penetrate deeper. They also carry more momentum, which makes them less likely to be affected by wind or small obstructions like grass.

To find the ideal arrow weight, you need to consider your specific goals and hunting conditions. Different game animals require different approaches. For instance, when hunting bigger animals like elk, heavier arrows are often preferred due to their increased penetration and ability to handle larger bones. On the other hand, lighter arrows are favoured for animals like whitetail deer, as they are faster and give the animal less time to react.

It's important to remember that increasing arrow weight will result in a decrease in speed. As a rule of thumb, for every 3 grains of additional arrow weight, you can expect to lose approximately 1 foot per second (fps) of arrow speed. However, this relationship is not linear, and the exact speed loss will depend on various factors, including your bow's efficiency.

To optimise your setup, you should aim for a balance between speed and weight. This means finding an arrow weight that provides sufficient speed while still maintaining the necessary penetration and accuracy for your specific hunting needs.

One popular approach is to follow the "Golden Rule of Arrow Building", which suggests shooting the heaviest arrow that can maintain speeds between 270 and 280 fps. This range is believed to offer the best combination of speed, accuracy, and penetrating power. However, it's important to note that this rule may not apply to all setups, and customisation is crucial.

To fine-tune your setup, you can use online calculators and resources like the Arrow Efficiency Calculator, which takes into account factors such as draw length, draw weight, and arrow weight to provide estimates for arrow speed, kinetic energy, and momentum. Additionally, you can conduct field tests to gather real-world data and make informed adjustments to your setup.

Remember, there is no one-size-fits-all solution, and the "right way" is what works best for you, your equipment, and your hunting conditions. By understanding the relationship between arrow speed and weight, you can make informed decisions to optimise your archery performance.

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**How to calculate arrow speed**

There are several methods to calculate arrow speed. The most accurate method is to shoot your hunting arrow through a chronograph. However, if you don't have access to a chronograph, there are other ways to estimate arrow speed.

One method is to use an arrow speed calculator. These calculators take into account various factors that affect arrow speed, such as draw weight, draw length, arrow weight, and bowstring weight. For example, for every 10 lbs of draw weight reduction, raw arrow speed is typically reduced by 15-20 fps. Additionally, a longer draw length creates a longer power stroke, resulting in an increase in raw arrow speed of approximately 10-15 fps per added inch.

**Another method to estimate arrow speed without a chronograph involves the following steps:**

- Shoot a group of three arrows from 20 yards using your 20-yard pin.
- Find the center of the group and mark it.
- Shoot another group of arrows at the same target from 40 yards, using the same 20-yard pin.
- Find the center of the second group and measure the distance between the two marks.
- Use the formula: Speed=distance / Square root(arrow drop/16) to calculate your arrow speed.

It's important to note that the above method may not yield highly accurate results, but it can give you a reasonable estimate of your arrow speed.

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**How to calculate momentum and kinetic energy**

When it comes to archery, the two most important factors in discussing the penetrating ability of an arrow are its kinetic energy and momentum. Kinetic energy is the "power potential" of the arrow at the target, derived from the Greek "kinesis", meaning motion, and "energeia", meaning active work. Thus, kinetic energy can be understood as "active work through motion".

Kinetic energy is calculated using the formula: Kinetic Energy (ft./lbs.) = Mass (total arrow weight) x Velocity (arrow speed)^2 / 450,240. For example, if you have an arrow that weighs 400 grains and is flying at a speed of 290 feet per second, the kinetic energy would be calculated as 290 x 290 x 400 / 450,240 = 74.72 foot-pounds of kinetic energy.

Momentum, on the other hand, can be defined as "mass in motion". In physics, momentum is the property of a moving object to continue moving. The formula for calculating momentum is: Momentum (p) = Mass (m) x Velocity (v). For example, a 429-grain arrow flying at 287 feet per second would have a momentum of 0.547 slug-ft/s.

It's important to note that while both kinetic energy and momentum involve calculations of mass and weight, they are not interchangeable. Kinetic energy can be thought of as the "big hammer", while momentum represents the ability to put that power to work, or the "nail" being driven through the target. Kinetic energy favors arrow speed, while momentum favors weight.

When it comes to archery, the goal is to find the right balance between kinetic energy and momentum to achieve the desired penetration and accuracy. Heavier arrows generally provide greater momentum and deeper penetration, while lighter arrows at high velocity have more kinetic energy. The challenge is to optimize speed, range, arrow mass, and penetration potential.

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**Frequently asked questions**

The formula for calculating momentum is: p (momentum) = m (mass) x v (velocity).

The momentum of an arrow is influenced by its mass and velocity.

Kinetic energy is the "power potential" of the arrow, while momentum can be thought of as the ability to put that power to work, i.e., penetrate the target.

To calculate the momentum of an arrow, you need to know its mass (weight in grains) and its velocity (speed). You can then use the formula mentioned above to calculate momentum.