The Flimsy AcceleroMeter: Principle of Operation

Joachim Köppen DF3GJ Kiel/Strasbourg/Illkirch Winter 2004

Design Philosophy

The FAM is a simple accelerometer which can be constructed with easily available material and which should give an indication of weightlessness rapidly enough and accurately enough to enable simple measurements in an indoor Drop Tower (drop of 2 m height). It is also capable of giving a rapid and easily visible optical indication when the weight is reduced below a certain value.

It is constructed from

• a piece of printed circuit board,
• coiled springs,
• pieces of copper wire used for low voltage applications,
• a sewing pin,
• some cardboard,
• a light emitting diode, two 1.5 V batteries, and some more wire

Version

The instrument described here is the 4th of a number of rather different designs, and has been verified to achieve the design goals.

Why and how it works

The weight (i.e. the gravitational acceleration) of a small mass M on a long arm L1 is counterbalanced by the elastic restoring force from two counteracting coiled springs S which acts on the short arm L2. This is essentially a spring balance, and the pointer P indicates the weight of the mass.

Some details:

• two springs are used so that the balance covers the entire range from 0 to 1 g with the same sensitivity, and is even capable to measure negative accelerations, i.e. accelerations upwards
• by using a short arm L2 for the springs to act on, their small displacement is magnified into a large displacement of the long pointer P.
• since the arm L2 is shorter than arm L1, a small mass M suffices to make a displacement of the springs
• by being fixed on the arm L2, the mass M can only move on a circle of radius L2. It does not respond to accelerations that are parallel to the axis A of rotation.
• in an earlier design, the mass was fixed to one of the springs. This leads to a sideways displacement of the springs when undergoing sideways accelerations. The present design is insensitive to this effect.

However, some approximations had to be accepted:

• the mass M moves on a circle: Ideally it should be allowed to move only in vertical direction, if one wants to measure vertical accelerations only. But as we shall use it only in the Drop Tower, this is o.k.
• the linkage of the short arm L2 to the spring armature SA between the two springs is at the end of the arm. Hence it will move on a small circle about the axis A, which causes the arm to raise SA and so the inner ends of the springs as the arm moves away from the vertical. The springs are not only compressed or extended in their length, but move also sideways. This will cause some additional friction at the springs' end points, and also a downward force on the axes and its bearings with more friction.

• Construction of Main Body
• Calibration
• Adding Visual Indication
• Analysis