There is a lot of advice and information available on the internet regarding the way projectiles fly high or low when fired into a crosswind. Unfortunately, when it comes to pellets, most of the information is wrong. Here I hope to try to explain why pellets fly high or low in a crosswind and why bullet derived diagrams are not suitable for the majority of pellets.
When a pellet is fired from a gun with a crosswind blowing across the trajectory, there are two distinct effects. The main effect is the downwind drift, which was described in this thread:- https://www.airgunnation.com/threads/how-wind-causes-pellets-to-drift.1278969/
There is a second effect, usually called the vertical error or vertical effect. Contrary to popular myth, despite what you may read on the internet, it is not caused by Magnus. It is simply a result of gyroscopic stability. It will help to understand what causes vertical error if you have seen the previous thread on pellet gyroscopic stability:- https://www.airgunnation.com/threads/gyroscopic-stability.1277792/
When a pellet leaves the barrel of an air gun, it is pointing more or less in the same direction as the gun barrel. If there is no wind then the airflow, due to the pellets speed, is coming directly at the pellet. If there is a crosswind, the airflow direction is changed slightly so that now it is coming at a small angle to the pellet as shown in this figure. The airflow the pellet sees is in the direction of the green arrow.
A stable pellet will always try to face into the direction of the airflow it sees, this is the definition of a stable pellet. It does not try to keep pointing in the direction it is facing when it left the barrel. Because, on leaving the barrel the pellet is not facing into the airflow, the air passing around the pellet will create a side force on the pellet.
The side force actually acts all over the pellet with many separate small forces, the size and direction of each force at each point depending on the shape of each part of the pellet. For convenience, we only consider the total side force and the point through which it has to act to reproduce the same effect as all the separate forces. The point through which the aerodynamic side force acts is known as the centre of pressure (CP), which on most pellets lies behind the centre of gravity (CG). When the CP is behind the CG, a pellet is said to be aerodynamically stable as the aerodynamic moment created by the aerodynamic side force is trying to turn the pellet to face the airflow.
This is where most pellets differ from bullets and slugs, in that for bullets and slugs the CP is in front of the CG creating a destabilizing aerodynamic moment which moves the bullet/slug away from the direction of the airflow.
The aerodynamic moments are important because objects which are spinning at high speeds will only change their orientation as a reaction to a moment, not a force. Side forces will move a spinning body sideways but, unless they are also producing a moment about the CG, forces will not change the orientation. The gyroscopic reaction to an aerodynamically unstable projectile is in the opposite direction to that of an aerodynamically stable one. This is what makes most pellets react differently to a bullet/slug in a crosswind, and is the reason charts for bullets cannot be used for pellets.
Combining two of the above diagrams shows how the crosswind produces a side force on the pellet which, because it acts through the CP, produces an aerodynamic moment about the CG.
The gyroscopic reaction to the aerodynamic moment is to cause the pellet nose to rise in the case shown where the wind is blowing left to right from the nine o’clock position. Looking at the front of the pellet along the green line above, we see it as the airflow will see it.
As mentioned previously, if we have a bullet or a slug the gyroscopic reaction will be in the opposite direction i.e. nose down, due to them having a destabilizing aerodynamic moment.
The nose up reaction of the pellet will produce a vertical force slightly changing the direction of the pellet, which is what produces the vertical error at the target. If the wind is coming from the right, i.e. three o'clock, the pellet will turn nose down and the force direction will be downwards.
The vertical force in turn produces a stabilizing aerodynamic moment which causes a gyroscopic reaction on the pellet, turning it to face into the airflow, which will reduce the aerodynamic forces and moments allowing the pellet to face directly into the airflow.
Because the vertical force only acts on the pellet for a short time immediately after it leaves the gun barrel the deflection in the trajectory is linear i.e. it increases directly with range. The down wind drift however increases in a non-linear fashion, getting much greater as the range increases.
The vertical error is often expressed as a percentage of the down wind drift. This is a very simplified way of looking at it and is not correct, as the ratio between the vertical error and the down wind drift changes depending on the range. Below is a diagram showing how the ratio changes with range for a .22 pellet fired at 900ft/sec into a constant 5mph cross wind over the entire distance to the target.
It is the shape of the curve that is of interest. The waviness of the curve is the result of heave and swerve (spiralling) giving small changes in the pellet position. At short ranges the ratio is very high but the actual drift height errors are very low so you are unlikely to notice it. The diagram below shows the values of the errors in inches for the pellet trajectory above.
The short range ratio values are also heavily distorted by the effects of heave and swerve, and the modelling is least accurate near the gun as it is trying to predict the rate at which the pellet turns to face the airflow. It is only at longer ranges that the vertical error may become a problem, despite being a smaller value compared to the down wind drift. The main point of showing the ratio curve is to show that the ratio is not a constant value between the downwind drift and the vertical error over the entire range, as sometimes claimed.
The size of the vertical error and the ratio between the vertical and down wind errors from a crosswind will depend on your chosen rifle and pellet. Practising with your chosen rifle and pellet will show you if it is something you need to take into account at longer ranges. Some shooters notice it, others have never seen any change and deny it exists, but there is photographic evidence that pellets suffer from the effects the same as bullets. Long range target shooters seem to be the ones who mainly notice it, and who sometimes go to extreme lengths to try to reduce it to a minimum.
When a pellet is fired from a gun with a crosswind blowing across the trajectory, there are two distinct effects. The main effect is the downwind drift, which was described in this thread:- https://www.airgunnation.com/threads/how-wind-causes-pellets-to-drift.1278969/
There is a second effect, usually called the vertical error or vertical effect. Contrary to popular myth, despite what you may read on the internet, it is not caused by Magnus. It is simply a result of gyroscopic stability. It will help to understand what causes vertical error if you have seen the previous thread on pellet gyroscopic stability:- https://www.airgunnation.com/threads/gyroscopic-stability.1277792/
When a pellet leaves the barrel of an air gun, it is pointing more or less in the same direction as the gun barrel. If there is no wind then the airflow, due to the pellets speed, is coming directly at the pellet. If there is a crosswind, the airflow direction is changed slightly so that now it is coming at a small angle to the pellet as shown in this figure. The airflow the pellet sees is in the direction of the green arrow.
A stable pellet will always try to face into the direction of the airflow it sees, this is the definition of a stable pellet. It does not try to keep pointing in the direction it is facing when it left the barrel. Because, on leaving the barrel the pellet is not facing into the airflow, the air passing around the pellet will create a side force on the pellet.
The side force actually acts all over the pellet with many separate small forces, the size and direction of each force at each point depending on the shape of each part of the pellet. For convenience, we only consider the total side force and the point through which it has to act to reproduce the same effect as all the separate forces. The point through which the aerodynamic side force acts is known as the centre of pressure (CP), which on most pellets lies behind the centre of gravity (CG). When the CP is behind the CG, a pellet is said to be aerodynamically stable as the aerodynamic moment created by the aerodynamic side force is trying to turn the pellet to face the airflow.
This is where most pellets differ from bullets and slugs, in that for bullets and slugs the CP is in front of the CG creating a destabilizing aerodynamic moment which moves the bullet/slug away from the direction of the airflow.
The aerodynamic moments are important because objects which are spinning at high speeds will only change their orientation as a reaction to a moment, not a force. Side forces will move a spinning body sideways but, unless they are also producing a moment about the CG, forces will not change the orientation. The gyroscopic reaction to an aerodynamically unstable projectile is in the opposite direction to that of an aerodynamically stable one. This is what makes most pellets react differently to a bullet/slug in a crosswind, and is the reason charts for bullets cannot be used for pellets.
Combining two of the above diagrams shows how the crosswind produces a side force on the pellet which, because it acts through the CP, produces an aerodynamic moment about the CG.
The gyroscopic reaction to the aerodynamic moment is to cause the pellet nose to rise in the case shown where the wind is blowing left to right from the nine o’clock position. Looking at the front of the pellet along the green line above, we see it as the airflow will see it.
As mentioned previously, if we have a bullet or a slug the gyroscopic reaction will be in the opposite direction i.e. nose down, due to them having a destabilizing aerodynamic moment.
The nose up reaction of the pellet will produce a vertical force slightly changing the direction of the pellet, which is what produces the vertical error at the target. If the wind is coming from the right, i.e. three o'clock, the pellet will turn nose down and the force direction will be downwards.
The vertical force in turn produces a stabilizing aerodynamic moment which causes a gyroscopic reaction on the pellet, turning it to face into the airflow, which will reduce the aerodynamic forces and moments allowing the pellet to face directly into the airflow.
Because the vertical force only acts on the pellet for a short time immediately after it leaves the gun barrel the deflection in the trajectory is linear i.e. it increases directly with range. The down wind drift however increases in a non-linear fashion, getting much greater as the range increases.
The vertical error is often expressed as a percentage of the down wind drift. This is a very simplified way of looking at it and is not correct, as the ratio between the vertical error and the down wind drift changes depending on the range. Below is a diagram showing how the ratio changes with range for a .22 pellet fired at 900ft/sec into a constant 5mph cross wind over the entire distance to the target.
It is the shape of the curve that is of interest. The waviness of the curve is the result of heave and swerve (spiralling) giving small changes in the pellet position. At short ranges the ratio is very high but the actual drift height errors are very low so you are unlikely to notice it. The diagram below shows the values of the errors in inches for the pellet trajectory above.
The short range ratio values are also heavily distorted by the effects of heave and swerve, and the modelling is least accurate near the gun as it is trying to predict the rate at which the pellet turns to face the airflow. It is only at longer ranges that the vertical error may become a problem, despite being a smaller value compared to the down wind drift. The main point of showing the ratio curve is to show that the ratio is not a constant value between the downwind drift and the vertical error over the entire range, as sometimes claimed.
The size of the vertical error and the ratio between the vertical and down wind errors from a crosswind will depend on your chosen rifle and pellet. Practising with your chosen rifle and pellet will show you if it is something you need to take into account at longer ranges. Some shooters notice it, others have never seen any change and deny it exists, but there is photographic evidence that pellets suffer from the effects the same as bullets. Long range target shooters seem to be the ones who mainly notice it, and who sometimes go to extreme lengths to try to reduce it to a minimum.
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