The tape measure
Why does it stand out stiff, then snap back in?
The question
A tape measure's blade is thin steel, yet it sticks straight out on its own. Let it go and it zips back into the case. How?
Have a guess, then show the answer
The blade is curved across its width, and that curve keeps it stiff, until it is out so far that the curve gives way and it buckles. Inside the case, a flat coiled spring winds tighter as you pull, and unwinds to reel the blade home.
Play
Pull the blade out, then let it go
This is a tape measure from the side, with its case cut open. Drag the blade end to the right, or use the slider, and push it past its stand-out. Then switch to a flat blade. Turn the lock on to hold the blade, and off to let the spring take it back.
Drag the blade end to the right, or use the slider. Then let go.
Hooked over an edge and pulled, the loose hook slides out by its own thickness, so its inside face lands on zero.
What's happening
- 1
Look at the end of the blade. The steel is curved across its width.
- 2
Like a strip of paper, flat, it flops. Curve it, and it holds. The curve keeps the blade stiff and straight when it's out.
- 3
How far it can stick out before it buckles under its own weight is called its stand-out. Push past that and the curve gives way.
- 4
Inside the case, a flat coiled spring winds tighter as you pull. A lock presses on the blade to hold it. Unlock it, and the spring unwinds, reeling the blade home.
- 5
The loose hook at the end slides by its own thickness, so inside and outside measurements both start from true zero.
Simplified, and sources
The drawing is simplified, and its lengths are made up. The sources define stand-out but don't give a length, so the stand-out line is only illustrative, and so is how much stiffer the curved blade is than the flat one. The bending comes from a simple beam formula that is only exact for small sags. The buckle is drawn at one fixed point, the hook is enlarged and its slide exaggerated, and the blade is reeled home faster the further out it is, which is a simplification of how the spring really pulls.