Tag Archive: math


So I did some of the math today. Problem with the go-kart actually going is definitely gears. We’re waaayyyyyyyyyyy too low of a ratio at the moment. Sure, more power would solve the problem easily. However, let’s look at the math:

6000 RPM electric motor
20″ diameter tires
14:60 drive ratio (~4.28)

6000 RPM input / 4.28 motor:axle ratio = 1401.869 axle RPM; let’s call it 1402. So axle (and tires) are doing 1402 RPM at max motor speed (which is where DC motors run the best/coolest/most efficiently).

20″ diameter * 3.14159 = 62.832 inch circumference of the tire.

62.832 / 12 inches per foot = 5.236 foot circumference

1402 RPM * 5.236 feet/rev = 7340.872 feet/min

See the problem yet?

60 MPH = 1 mile per minute

1 mile = 5280 feet            DING-DING-DING-DING-DING! You should see the problem by now……

7340.872/5280 = 1.3903 miles/minute * 60 miles/hour = 83.419 miles/hour

We do NOT need to be tearing around at practically 85 miles an hour on a go-kart when the motor is running at its best! I’m not sure what to do about correcting this myself; perhaps others have ideas on how to just about double the drive ratio? What’s the best way to go from 4.28:1 ratio to something more like 9:1?

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Happy Pi Day(s)!

As many know, and many don’t, yesterday was ‘Pi Day’ according to the Gregorian (normal) calendar. March 14th, 3/14, aligns with the first two decimals of the number π, 3.14. It also happens to be the birthday of Albert Einstein. Personally, I take it as a two-day celebration. π is 3.1415 to four decimals, so why limit it to the 14th? Celebrate 3/14/15!

So if you didn’t know about it yesterday, redeem yourself. Have some Pi(e) today and think on the ratio of its circumference to its diameter.

We had pot pie for dinner last night and pie for dessert. Tonight I shall watch the movie π. Enjoy!

Binary Days

2010 and 2011 are unique years, truly. Well, any ’10’ and ’11’ years are, but I doubt I, readers, or this blog, will be around to see 2110 or 2111. Why are they so special? They’re the years of binary days! The months of January, October, and November in 2010 and 2011 have days where every digit of the date is a 1 or a 0. These can be converted to decimal as they stand; but some of the fun comes in converting from binary to ASCII – American Standard Code for Information Interchange. By adding a leading zero, we can take the two-digit dates and look at them in all three formats. Here’s a table of all the binary days for you to enjoy!

23

Date Binary Adjustment Decimal Equivalent ASCII Character Equivalent
01/01/10 0010110 22 Ctrl+V (SYN command; now used as ‘Paste’)
01/10/10 0011010 26 Ctrl+Z (SUB command; now used as ‘Undo’)
01/11/10 0011110 30 Ctrl+^ (RS command; used in AS/400 systems)
10/01/10 0100110 38 ‘&’ (Ampersand)
10/10/10 0101010 42 ‘*’ (Asterisk)
10/11/10 0101110 46 ‘.’ (Period)
11/01/10 0110110 54 ‘6’ (The six digit)
11/10/10 0111010 58 ‘:’ (Colon)
11/11/10 0111110 62 ‘>’ (‘Greater Than’ sign)
01/01/11 0010111 23 Ctrl+W (ETB command; used in AS/400 systems)
01/10/11 0011011 27 Ctrl+] (ESC command; now accessed from the Escape key)
01/11/11 0011111 31 Ctrl+_ (US command; used in AS/400 systems)
10/01/11 0100111 39 ”’ (Single quote)
10/10/11 0101011 43 ‘+’ (Plus sign)
10/11/11 0101111 47 ‘/’ (Forward slash)
11/01/11 0110111 55 ‘7’ (Seven digit)
11/10/11 0111011 59 ‘;’ (Semicolon)
11/11/11 0111111 63 ‘?’ (Question Mark)

Battery Math

When it comes to EV building, you can have the best of the best of everything – aerodynamic body, great motor, excellent controller. However, when it’s all said and done, you’ll sink or swim depending on your batteries.

I’m not going to get into types/sizes/brands here; this is more about the preliminary calculations than anything else. There are some general rules of thumb when it comes to powering an EV:

  • Voltage = Speed. It’s not quite that simple, but close enough for basics. The more voltage you can provide to the motor, the faster you’ll be able to go.
  • Amperage = Acceleration. Whereas voltage enables the motor to turn faster, amperage is what allows the motor to turn when a load (in our case, a whole car via the driveshaft) is applied.

Also to note is the fact that the lower the amperage you ask the batteries to output, the longer they can output it for. This means you either accelerate VERY slowly, or…increase the voltage!

How does that work, if voltage equals acceleration? It’s a transformation of Ohm’s Law. Ohm’s Law states that the current, I, through a conductor between two points is directly proportional to the potential difference, V, across the two points, and inversely proportional to the resistance, R, between them:

I=\frac{V}{R}

Current is amps, “Potential Difference” is volts, and the resistance is the load/work we want the electricity to be doing – realistically, the wattage. So to simplify, we end up with the following replacements and transformation:

\mbox{Amps}=\frac{\mbox{Volts}}{\mbox{Watts}}              THUS             \mbox{Watts}=\frac{\mbox{Volts}}{\mbox{Amps}}

So, for the same amount of power output (in Watts), I can have more amps and less volts, or more volts and less amps. Less amps = good things, so we keep the voltage as high as reasonably feasible.

I’ve got 64x 12V, 7.2Ah batteries. They’re small, both in electrical capacity (amp-hours), and in physical size. However, there are SIXTY-FOUR of them.

That’s the same as 8x 96V 7.2Ah batteries.
8x 7.2Ah = 57.6 Ah total @ 96V
96V * 57.6Ah = 5529.6 Wh; 5.5296 kWh

There are 5.52 kilowatt-hours of electricity in my battery pack. Electric cars use, on average, 250 to 350 Watt-hours of electricity per mile driven.

Let’s use 300 Wh/mi for now, with an 80% ‘Depth of Discharge.’ That’s how much of the total power you use out of the batteries. If you 100% discharge a battery, it’ll basically kill it permanently. 80% is a “safe zone” of discharge for lead-acid batteries, so let’s start there.:

5529.6Wh * 0.80 DoD = 4423.68 Wh @ 80%
4423.68Wh / 300Wh/mi = 14.746 miles

so yeah, we’ll call it 15 miles range at 80%. Most likely, with used batteries like mine, it’d be safer to only go to 50% – which works out to 9.218 miles. The batteries I have are extremely small! Most EV-ers have batteries that are 20 to 60 Amp-hours EACH! This is why we’re starting with the go-kart.