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How to check the flatness and squareness of a plane
According to the British Standard for bench planes, the sole of a plane shall be flat to a maximum total deviation of 3 thousandths of an inch on centreline, the sides of the plane shall be square to the sole to within a tolerance of 30 minutes (half a degree).
To inspect the condition of a plane you need a straightedge that is longer than and substantially more accurate than the surface you are inspecting with reference to it. A 24 inch straightedge conforming to BS5204 grade B will be straight to better than 0.47 thou, the equivalent German standard is DIN874/1. These are the bare minimum standards required in order to measure how flat the sole of a plane is, if you can avail yourself of a BS5204 grade A or DIN874/0 or 00 straightedge for the purpose, so much the better. Comparing the sole of a new plane with an unmarked £25 ‘precision straightedge’ will probably tell you more about the ‘precision straightedge’ than it will about the plane.
In order to measure whether any gap between the straightedge and the sole of the plane exceeds tolerance, you will need to use a 3 thou (or 0.075mm) feeler gauge. With the plane inverted and supported to keep it level, sit the straightedge on top and gently try to introduce the feeler gauge underneath it. If it deflects then any gap existing between the two is less than three thou, if it slides cleanly underneath then the gap is greater than three thou.
Being able to see light under a straightedge confirms nothing, because light has no definable thickness. To put this into perspective, an optic fibre core has an external diameter of 8 microns or 0.3 thou, which is one tenth the size of the potential gap we are trying to measure.
Ideally a plane should also be inspected against a surface plate of similar accuracy to the straightedges mentioned previously. In this case the plane is placed on top of the surface plate and the feeler gauge is tried around the sole, bear in mind when doing this that the sharp corners of the sole will have been eased slightly to avoid them catching on the workpiece.
Checking the sides of the plane for squareness is a similar process; you will need a square that is accurate to BS939 grade B (DIN 875/1) or better. For a 4 inch or 100mm square this is a maximum deviation of 0.63 thou or 16 microns.
Angles are measured in degrees and each degree is subdivided into 60 minutes. The tolerance for bench plane squareness is 30 minutes or half a degree. The tolerance we are measuring against is therefore the tangent of 0.5 degrees multiplied by the distance from the apex of the square.
In plain English this means 8.7 thou or 0.22mm twixt plane and square measured 1 inch away from the corner, or twice that much measured two inches away. Again this should be established using feeler gauges.