Topic 4 - External Ballistics

Question 1

What dictates the path of a projectile?

Answer 1

• Gravity
• Angle of launch
• Velocity
• Air density, temperature & humidity
• Projectile shape (drag coefficient & projectile stability)

Question 2

What SUVAT equation would you use for a horizontal launch (zero-degree elevation so the trajectory starts at its maximum height) for the y-direction?

Answer 2

S = ut + 1/2at^2
u = 0 so s = 1/2 at^2

Question 3

What equation could you use in the x-direction when there is no air resistance and no deceleration?

Answer 3

Ux = Sx / Ttotal

Question 4

What suvat equation can be used if the launch and impact sites are on the same horizontal plane?

Answer 4

S = (u^2sin(2angle) / g

Question 5

What is aerodynamic drag typically proportional to?

Answer 5

Aerodynamic drag is typically proportional to the square of the velocity, so drag builds significantly with velocity.

Question 6

What factors contribute to drag?

Answer 6

• The profile or shape of the projectile.
• The cross-sectional area of the projectile in the direction of travel.
• Air density.

Question 7

What is the centre of mass (also known as the center of gravity / CoM / CoG)?

Answer 7

The point where the bullet balances its weight
Like the pivot point on a see-saw

Question 8

What follows the trajectory when in flight?

Answer 8

The center of mass is the only point of the bullet that follows the trajectory when in flight.

Question 9

What is the center of pressure (CoP)?

Answer 9

The center of pressure is the point where the aerodynamic forces act after adding up all of them.
In the case of a bullet, it will be the sum of the drag forces from the air flow.

Question 10

How is drag stabilisation acieved?

Answer 10

• By adding fins which creates additional drag forces at the rear of the projectile.
• This brings the CoP rearward of the CoM leading to a smaller and less influential turning moment.
• This results in a stable flight path without the need for and gyroscopic stabilisation

Question 11

How can the total drag force experienced by a projectile be calculated?

Answer 11

Fd = 1/2CdAV^2p

Fs = Drag force in n
Cd = Drag coefficient
V = flow velocity in m/s
A = cross-sectional area
p = air density @ sea level (about 1.2 kg/m^3)

Question 12

What can wind tunnels be used to measure?

Answer 12

Wind tunnels can be used to measure the drag force experienced by a projectile design as air is blown over a stationary object.

Question 13

How do you calculate drag coefficient (Cd)?

Answer 13

Cd = 2Fd / AV^2p

Question 14

What is the Mach number?

Answer 14

It defines how many times the speed of sound the projectile is moving at?

Question 15

How do you calculate sectional density?

Answer 15

S = m /d^2

Question 16

What is the ballistic coefficient?

Answer 16

The measure of the aerodynamic forces exerted on a particular bullet in flight, known as Cb.

Question 17

What unit is Cb?

Answer 17

kg/m^2

Question 18

What is Cg?

Answer 18

Cg = Drag coefficient of the G1 standard projectile = 0.5191

Question 19

What is one of the major contributors to modern projectile accuracy?

Answer 19

Gyroscopic stabilisation (also known as spin)

Question 20

What is the amount of lift proportional to?

Answer 20

The amount of lift is proportional to the air speed over the surface and the rate or curvature.

Question 21

What are the two main types of wind deflection?

Answer 21

• Aerodynamic
• Windage

Question 22

What is rifling-induced instability caused by?

Answer 22

A low spin rate

Question 23

What are the 3 main causes of a low spin rate?

Answer 23

• Low muzzle velocity
• High muzzle velocity
• Defective rifling

Question 24

What does yaw refer to?

Answer 24

Yaw refers to the lateral movement of the nose of the bullet away from the line of flight.

Question 25

What does precession refer to? COM

Answer 25

Precession refers to the rotation of the bullet
around the centre of mass

Question 26

What does nutation refer to?

Answer 26

Nutation refers to small circular movements at
the bullet tip due to the tip not being perfectly round.

Question 27

When do yaw and precession decrease?

Answer 27

Yaw and precession typically decrease as the distance of the bullet from the barrel increases, since gyroscopic stability will keep them under control.

Question 28

What are the main causes of yaw?

Answer 28

• A poorly cast bullet or bad loading, causing the bullet to be off-centre in the cartridge case neck.
• Irregular rifling or non-optimal spin rate.

Question 29

What is windage?

Answer 29

• Windage: Deflection caused by constant wind pressure during projectile flight.
• A strong breeze can cause several metres of deflection at longer ranges.

Question 30

What is aerodynamic wind deflection?

Answer 30

Aerodynamic: Caused by wind flow over the projectile in flight, generating more lift on one side of the bullet due to spin induced
pressure difference.
* This effect is very small and only shows up at very long range.

Question 31

What type of wind deflection has a stronger effect?

Answer 31

• Windage
• This has a much more pronounced effect on the overall trajectory.
• A strong breeze can cause several metres of deflection at longer ranges.

Question 32

How does low muzzle velocity lead to a low spin rate?

Answer 32

• The bullet engages with the rifling but never reaches a spin rate that will ensure stability. — This could be caused by a low or defective charge, excessive bore friction, or a bullet of incorrect calibre being used in the firearm.

Question 33

How does high velocity lead to a low spin rate?

Answer 33

• This is particularly seen with unjacketed bullets.
• The bullet velocity may be so high that the soft bullet skids over the rifling.
• This is typically caused by a hand-loaded round or an incorrect bullet choice. This can lead to distinctive rifling marks.

Question 34

How does deflective rifling lead to a low spin rate?

Answer 34

The bullet fails to engage with the worn or defective rifling, leading to a low spin rate, aerodynamic imbalance and potential tumbling.