Slope 1:5
A 1:5 wedge has been driven under a machine bed, a load placed on top and the hammer taken away. With dry faces the wedge stays put. A drop of oil is enough — and it shoots back out with a click. A 1:5 slope has an angle of 11.3°, and a wedge holds as long as that angle is less than two friction angles. For dry steel that is about 11.4°: the margin is a tenth of a degree.
Slope is the ratio of the rise to the length over which it is gained, a number without a unit. 1:5 means that over every 5 mm of length the face rises by 1 mm. Slope is measured on one side, and that is what sets it apart from taper, which is measured on the diameter, on both sides at once. That is why a cone whose generatrices have a 1:10 slope has a taper of 1:5.
| Notation | i — slope, written ∠1:n · β — angle of the face to the base |
| Definition | i = (H − h) / l = tan β; taper C = 2i |
| Notation | GOST 2.307: the ∠ sign before the ratio; in construction — %, ‰ or degrees |
| Self-locking of a wedge | the wedge holds by itself if β < 2ρ: dry steel μ ≈ 0.1 — up to 11.4°, lubricated — up to 5.7° |
| Mechanical advantage | without friction 1/i: a 1:5 wedge is pushed with 5 times less force than it lifts |
| Typical values | taper key 1:100 · slideway gib 1:50 · casting draft 1:20 · channel flange 1:10 · forging wedge 1:5 |
01 · Definition
The rise of one face over a length
A slope is specified for one surface relative to another — the base. On the drawing the ∠ sign and the ratio are placed on the leader landing; the acute angle of the sign shows which way the face goes down. Two dimensions are given together with the slope, usually the height at the thick end and the length; the third is obtained by calculation.
A wedge is an inclined plane turned into a part: a pushing force F produces a force of about F/i on the face. The price is paid in travel: to lift a load by 1 mm, a 1:5 wedge is pushed in by 5 mm. The same load pushes the wedge back out, and only friction holds it. As long as the face angle is less than the sum of two friction angles, the wedge stays put by itself.
Slope versus friction
The rows are standard slopes. The bar is the face angle β, the vertical line is the self-locking limit 2ρ for the selected friction. Blue wedges stay put by themselves, red ones are pushed out by the load.
Five wedges, three kinds of friction, one load
The main action is the «Start check» button. First the dial indicator travels along the inclined face and measures the rise over the length — that is the slope. Then the wedge is driven with a hammer into the gap under the upper block, and the block rises. A load is placed on top and the hammer is taken away. If the face angle is less than two friction angles, the wedge stays put; if it is greater, the load pushes it out and the block drops. Below the scene you choose the wedge — a 1:100 key, a 1:50 slideway gib, a 1:20 shim wedge, a 1:10 wedge jack or a 1:5 forging wedge — and the friction on the faces: dry, steel on steel or lubricated. The slider rewinds the check.
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02 · Conversion
Quick reckoning: a 1:n slope is 100/n % and roughly 57.3/n degrees. 1:5 is 20% and 11.3°, 1:20 is 5% and 2.9°, 1:100 is 1% and 0.57°.
Percent and degrees part ways quickly: 100% is 45°, not 90°. A «12%» road sign means about 6.8°; a 1:1.6 staircase is already 32°.
| i | β | % | where |
| {k} | {v} | {h} | {n} |
03 · Orders of magnitude
04 · Measuring instruments
05 · Writing rules
Series · Drafting and CAD
desk tips for every sheet06 · Neighbouring units
07 · Historical section
Slope, like taper, is a ratio of two lengths, and it is measured with two lengths: the travel along the face and the rise. An indicator error of 0.01 mm over 100 mm of travel gives a slope error of 10⁻⁴. For a 1:5 wedge that is 0.05%, for a 1:100 key already 1%: a shallow slope is harder to measure.
Self-locking is a property not of geometry alone but of the pair «slope and friction». The friction coefficient of steel on steel wanders from 0.08 to 0.2 depending on cleanliness and lubrication, so wedges that must hold are made with a large margin — 1:100 for a key. A 1:5 wedge, on the contrary, is chosen when it has to be knocked out again: it works right on the limit.
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