NGC: Math puzzler

[Moto]

I have found instructions for calibrating my Italjet speedometer, as follows:

You need to adjust value F03.4 to calibrate the speedometer. The higher the number, the slower the actual readout is on the speedo. You should adjust the frequency according to your wheel. Such as, on a wheel with 81.375 inches circumference, and six magnets on the wheel, frequency is F08.0.

I can't figure out the relationship between 81.375 and F08.0. I'm presuming F08.0 is hex, which is equal to 3848 decimal. I've calculated the pulses per mile (4671.705) and per kilometer (2902.8648), but neither is close to 3848.

Obviously I can adjust my current setting (F05.7 = 3845.4375 decimal) by multiplying or dividing by the proportional error in the speedo reading, so this is an idle exercise, just a puzzler. Can anyone solve it?

Moto

[Aaron D.]

How many magnets on the wheel?

[Moto]

How many magnets on the wheel?

6.

[Rich A]

Wild guess: Does it have something to do with the relationship between F03.4 and F08.4?

Rich A

[Murray]

Would it be per 100 wheel rotations (or something similar).

[Moto]

Wild guess: Does it have something to do with the relationship between F03.4 and F08.4?

Rich A

Good idea. I think you meant F08.0, as given in the instructions? If not, why F08.4?

F08.0 = 3848 decimal

F03.4 = 3843.25 decimal

F08.0 - F03.4 = 4.C = 4.75 decimal

F08.4 - F03.4 = 5 = 5 decimal

I'm not seeing how your idea would work.

[Rich A]

Good idea. I think you meant F08.0, as given in the instructions? If not, why F08.4?

Typo, I meant F08.0. But I was thinking more along the lines of a ratio: F03.4/F08.0 or vice versa. Is one of those the ratio of 81.375 to whatever circumference the speedo was calibrated for?

Rich A

[Moto]

Typo, I meant F08.0. But I was thinking more along the lines of a ratio: F03.4/F08.0 or vice versa. Is one of those the ratio of 81.375 to whatever circumference the speedo was calibrated for?

Rich A

Seems possible. Let's see, the ratio F08.0/F03.4 = 3848 / 3843.25 =1.0012. But that is hardly an example ratio worth adjusting for!

Also, why would the circumference of only one of the two tires be given for the calculation in that case?

Moto

[Rich A]

Seems possible. Let's see, the ratio F08.0/F03.4 = 3848 / 3843.25 =1.0012. But that is hardly an example ratio worth adjusting for!

Also, why would the circumference of only one of the two tires be given for the calculation in that case?

Moto

I'm just guessing! And that isn't much of a difference. But the speedo must be calibrated for some specific circumference--whatever that is doesn't really matter in a sense; it's the ratio of the wheel/tire you're using relative to the standard that would determine the accuracy of the speedo for your application. Again, I'm just guessing.

[Moto]

I'm just guessing! And that isn't much of a difference. But the speedo must be calibrated for some specific circumference--whatever that is doesn't really matter in a sense; it's the ratio of the wheel/tire you're using relative to the standard that would determine the accuracy of the speedo for your application. Again, I'm just guessing.

I know you're just guessing! So are we all, I think.

 

[Zoom Zoom]

Why don't you just strap a GPS on long enough to adjust the speedo, get it perfect and be done with it??? Then remove the GPS.

ZZ

[Moto]

Why don't you just strap a GPS on long enough to adjust the speedo, get it perfect and be done with it??? Then remove the GPS.

ZZ

I will, as I think I implied at first. This is purely an "idle exercise, just a puzzler," to quote myself.

M.

[Moto]

I've got it! The value can be explained by a simple, one-character typo, followed by imperfect rounding of the result.

The tech started out to use 81 3/8 inches (81.375) as his example, likely from some real measurement since it is to the nearest 1/8 inch.

He then mistakenly typed 61.375 instead of 81.375 into his calculator or computer as he worked the formula for the number of pulses per kilometer, when there are 6 magnets.

That formula is f = d / (c / 6), where d is the length of a kilometer, c is the circumference of the tire, and (c / 6) is the distance the bike travels for each pulse. It is necessary to use the same units of measurement for both d and c, and he could have used inches or a metric unit without any problem. Supposing he used inches, d would be 39370.1, the number of inches in a kilometer, and c would be the typo, 61.375, instead of the intended 81.375.

The calculation with the typo works out to: f = 6 x 39370.1 / 61.375 = 3848.808147.

He then converted this decimal result to hex using a calculator that just drops fractional parts when it converts (like my Android calculator, e.g.). So he typed in 3848.808 (or so), and got back F08, rather than a more accurate F08.CED9, which he could have rounded up to F08.D had he obtained it.*

Then, being a nitwit, he reported F08.0 since his calculator said F08, and since he didn't see the implication of greater precision in adding the zero at the end. (Or maybe his calculator actually showed F08.0; mine shows F08, with no decimal point.)

In his write-up he used 81.375 as the circumference since he had not noticed his mistake with the calculator, and his erroneous result, F08.0.

It was Rich A.'s typo that made me think along the lines of a single mistyped digit. I then investigated both the mile and the kilometer as the distance, and found I could get the value in the instructions by changing an 8 to a 6 in the circumference.

Moto

*This site does the proper conversion: https://www.mathsisfun.com/binary-decimal-hexadecimal-converter.html .

[egschade]

Reading this makes my ear hair hurt. 

Good on you for figuring things out - you're a far better mathematician than I.

[Moto]

Reading this makes my ear hair hurt. 

Good on you for figuring things out - you're a far better mathematician than I.

 

Your own talents do not unnoticed, by the way: http://wildguzzi.com/forum/index.php?topic=97717.msg1544348#msg1544348

 

[Chuck in Indiana]

Attaboy, Moto..