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Therefore, regardless of the worm's size (sensible engineering limits notwithstanding), the gear ratio is the "size of the worm wheel - to - 1". Given a single-start worm, a 20-tooth worm wheel reduces the speed by the ratio of 20:1. With spur gears, a gear of 12 teeth must match with a 240-tooth gear to achieve the same 20:1 ratio.
For example, a transmission with an engine shaft to drive shaft ratio of 4:1 in first gear and 2:1 in second gear would be considered wide-ratio when compared to another transmission with a ratio of 4:1 in first and 3:1 in second. This is because the close-ratio transmission has less of a progression between gears.
High gear reduction ratios are possible in a small volume (a ratio from 30:1 up to 320:1 is possible in the same space in which planetary gears typically only produce a 10:1 ratio). Disadvantages include a tendency for 'wind-up' (a torsional spring rate) in the low torque region.
For example, if the static compression ratio is 10:1, and the dynamic compression ratio is 7.5:1, a useful value for cylinder pressure would be 7.5 1.3 × atmospheric pressure, or 13.7 bar (relative to atmospheric pressure). The two corrections for dynamic compression ratio affect cylinder pressure in opposite directions, but not in equal strength.
The designation of wide versus close ratio affected the lowest gear ratio; for example, the four-speed Muncie transmissions offered in General Motors performance vehicles included the M20 "wide ratio" transmission, which had a first gear ratio of 2.52 or 2.56:1, while the M21 and M22 "close ratio" transmissions had a first gear ratio of 2.20:1.
The golden ratio's negative −φ and reciprocal φ−1 are the two roots of the quadratic polynomial x2 + x − 1. The golden ratio is also an algebraic number and even an algebraic integer. It has minimal polynomial. This quadratic polynomial has two roots, and. The golden ratio is also closely related to the polynomial.
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