Game Development Reference
As you can see, the device consists of a known mass at the end of a spring next to a
measuring stick. When the elevator is not accelerating, the mass is at the 0 mark. When
the elevator accelerates up or down, the mass at the end of the spring resists that accel‐
eration and tends to stay at rest. This is Newton's first law in action. Inertial loading
causes the spring to stretch or compress. If the elevator is accelerating upward, the mass
will cause the spring to stretch downward. Recall from Chapter 3 that the force acting
on a spring is linearly dependent on the displacement of the mass via the equation:
F n = kd
We can directly measure the displacement, d , so we can determine the force in that
direction, n . As the mass is known, voilà!
a n = m/F n
As an aside, the fact that you can tell that you are accelerating without having to look
outside the elevator is what makes this a “noninertial frame of reference,” as discussed
in Chapter 2 . No worries if you don't totally understand that; it isn't important for what
we are discussing here.
Now, let's put our elevator back on earth. With the same device, the mass will not be at
0 even if the elevator is not accelerating because gravity is pulling it down. Previously
we used units of inches, which we then converted to force and finally to acceleration.
However, we now have a direct measure of the acceleration due to gravity and could
easily place a mark on where the mass is and call it 1 g . Also we could place marks along
the ruler at the same intervals. Now, we accelerate the elevator upward at 9.8 m/s 2 . The
mass should move down the scale to 2 g , and anyone standing in the elevator would feel
twice as heavy as normal.
Let's say we wanted to accelerate the elevator downward at 9.8 m/s 2 . We could easily do
this by just releasing the brakes and letting gravity do the work. Now in freefall we don't
feel gravity at all, right? That's because the downward acceleration is canceling the ac‐
celeration due to gravity. The mass will be back at 0 just like out in space, far from any
gravitational bodies. It is for this reason, and not a lack of gravity, that astronauts float
around. They are in freefall around the earth.
Lastly, if we accelerate the elevator downward at 2 g , the mass would move to the −1 g
mark on the ruler. This is because the downward acceleration is now overwhelming
gravity. Those in the elevator would find themselves standing on the ceiling feeling
exactly as they would standing on the ground! In fact, one of Einstein's accomplishments
was showing that it is impossible to distinguish gravity from inertial accelerations. We'll
leave the details of that for independent study and get back to accelerometers in the
form of MEMS.