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update Guide to be more structured and match the screenshot#327

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eugenesvk wants to merge 1 commit intoRawAccelOfficial:masterfrom
eugenesvk:fr-guide
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update Guide to be more structured and match the screenshot#327
eugenesvk wants to merge 1 commit intoRawAccelOfficial:masterfrom
eugenesvk:fr-guide

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  • layout text in more consistent and aligned tables
  • add guides to the picture that match the table values

To make it easier to follow and come back to when comparing with the app. So this

Then we have the following input parameters:

Parameter Value Unit Formula Calculation
$d$ distance $50$ counts $\sqrt{Δx^2 + Δy^2}$ $\sqrt{30^2 + 40^2}$
$t$ time $1$ ms $f^{−1}$ sec $1/1000$
$v_i$ velocity $50$ counts/ms $d/t$ $50/1$

transformation:

Parameter Value Unit Formula Calculation
$v_a$ accelerated
velocity
$1.5$ $(1 + av_i)$ $1 + 0.01⋅50$
$s_a$ accelerated
sensitivity
$0.75$ $v_a⋅m$
$≝v_o/v_i$
$1.5⋅0.5$

…and output:

Parameter Value Unit Formula Calculation
$v_o$ velocity $37.5$ counts/ms $s_a⋅v_i$ $0.75⋅50$

instead of

Then our input speed is $\sqrt{30^2 + 40^2} = 50$ counts/ms. Our accelerated sensitivity is calculated to be $(1 + 0.01 * 50) * 0.5 = 1.5 * 0.5 = 0.75$. So our output velocity is $0.75 * 50 = 37.5$. If I run the previous calculations with input speed 49.9 I get output velocity 37.40005, so our gain is about $\frac{37.5-37.40005}{50-49.9} = 0.9995$. Here is a picture of the charts in Raw Accel showing the same thing:

- layout text in more consistent and aligned tables
- add guides to the picture that match the table values
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