Handy way to assess the spin time changes you can expect from a given change in either release or critical speed in a given top:

Δ*t* = *t*_{2} - *t*_{1} = *T*_{1/e} ln(*ω*_{1} / *ω*_{2})

where (*t*_{1},*ω*_{1}) and (*t*_{2}, *ω*_{2}) are any 2 points on a purely exponential spin decay curve (SDC) such that *t*_{2} ≥ *t*_{1}, and *ω*_{1} ≥ *ω*_{2}. The "lifetime" *T*_{1/e} is the time needed for the top to lose 63.2% percent of any given starting speed.

**NB: **All times should be in seconds, but the speeds can be in either rad/s or RPM as long as they have the same units.

First measure any 2 (time,speed) points (*t*_{1},*ω*_{1}) and (*t*_{2}, *ω*_{2}) for the top of interest. Then rearrange the formula to determine its lifetime *T*_{1/e}. Then do the what-ifs with the formula as written above.

**Case 1: **Your current release speed is *ω*_{2}, but you hope to *increase* it to *ω*_{1}.

**Case 2: **Your current critical speed is *ω*_{1}, but you hope to *reduce* it to *ω*_{2}.

Note that when you double release speed or halve critical speed, *ω*_{1} / *ω*_{2} = 2, and ln(*ω*_{1} / *ω*_{2}) = ln 2 = 0.693. So either way, you'll extend spin time by 0.693 *T*_{1/e} seconds. For example, if *T*_{1/e} = 1,000 s (on the low side for a classic Simonelli), then doubling release speed or halving critical speed will add 693 s.

If you'd rather think in half-lives instead of lifetimes, the conversion is

*T*_{1/2} = *T*_{1/e} ln 2 = 0.693 *T*_{1/e}