Game Development Reference
In-Depth Information
Using Equation (5.34), an expression can be derived for the initial velocity,
v
a
, of an arrow when
the bow is released.
eFx
v
=
(5.35)
a
mkm
+
a
b
Arrows are long, fairly light objects, and as such the flight of an arrow will be strongly influ-
enced by wind and drag effects. The drag experienced by an arrow in flight has been measured
experimentally, and the drag was found to be a function of the velocity of the arrow squared
multiplied by a constant,
c
, that depended on the geometry of the arrow.
2
D
F v
=
(5.36)
For a typical medieval war arrow, the value of
c
would be 0.0001
N-s
2
/m
2
.
â–
Tidbit
An experienced medieval archer could aim and fire 10 arrows a minute. The English King Henry V
won the battle of Agincourt in 1415 even though he was outnumbered at least 4 to 1 because his 6000 archers
armed with longbows rained 60,000 arrows a minute upon the advancing French army.
Exercise
3.
If it takes 700
N
(154
lbs
) of force to draw a longbow back a distance of 0.5
m
, compute the initial velocity
imparted to a 0.06
kg
arrow when the bow is released. Assume that the longbow weighs 1
kg
, has an efficiency
factor of 0.9, and has a scaling factor
k
= 0.05.
Summary
We certainly have come a long way in this chapter. Starting with basic Newtonian mechanics
and kinematics, we developed a series of projectile trajectory models of increasing complexity.
We started with the gravity-only model, which as the name implies only considers the effects of
gravity on the projectile. The concept of aerodynamic drag was introduced. A formula was
presented that relates drag to the fluid density, object velocity, a characteristic area, and a drag
coefficient.
Wind effects were incorporated by having wind change the apparent velocity seen by the
projectile. Drag forces were then computed using the apparent wind velocities. The phenomenon
known as Magnus force was introduced whereby a lifting force is generated by a spinning object.
The value of Magnus force can be expressed as a function of a lift coefficient that has an analytical
form for simple shapes such as a sphere or cylinder.
The final part of the chapter gave details on some common types of projectiles—bullets,
cannonballs, and arrows. These sections gave the mass, velocity, and size data you can use to
simulate the flight of these projectiles.
