A Modest Proposal – The Case for a Parabolic Speedometer
 

I want a gauge that shows me velocity squared, what I'll call a parabolic speedometer. I've been kicking around this idea for a while, and I thought I'd bounce this off everyone here.

What good is velocity squared? After all, you can't use it to figure out how much time it takes to get somewhere. However, from a physics standpoint, velocity squared is crucial.

Two important quantities are related not to velocity, but to velocity squared – kinetic energy and aerodynamic drag. From a practical standpoint, this has a couple implications. It means that v², not v, determines how far you will climb up that upcoming hill. It means that v², not v, determines how much aerodynamic drag you'll experience – the predominant velocity-dependent loss. It means that v², not v, determines how bad an accident will be. How fast your v² dial goes up determines your power output, regardless of speed (unlike the current speedometer).

Ok, so maybe there's some dry physics implications behind a v² meter. How will that help me? Well, I can't count the times I've been coasting uphill to a long light, and I've either over- or under-shot it because of *tiny* changes in pulse speed at the bottom. Or going downhill I'll expect to pick up more speed than I do. And does anyone else find it hard to believe that drag at 75 mph is twice that at 53 mph? Even if you believe it, can you picture it? I know I can't.

Numerically, I think v² isn't very interesting. Miles squared per hour squared, anyone? Perhaps you could label it in vertical rise (in feet) by dividing by 14.962. This is probably the best you could get with a ScanGauge. Personally, I'd prefer to have something a little more spatial – a regular dial speedometer, complete with mph marks, that stretches out at higher speeds. I guess you could have a linear scale on the inside that shows rise distance as well.

Once I get my OBD2-USB adapter, I'll work on coding something up (Linux only, most likely).

Thoughts?

I definitely don't follow the part about rise. Let see how well I'm doing with the rest.

Let's assume the scale of your regular dial speedometer reads 0-110 mph.
Let's also assume that the needle sweep from 0-90 mph is 90*.
What do you want the needle sweep from 0-60 mph to be?

1. 60*
2. 40* (my understanding)
3. Some other number of degrees. (If so, what number?)

If the answer is 40*, I'd don't see why you'd need/want any additional scale markings other than km/h.

Sounds like you could do something like it with a regular speedometer with a partially covered long needle. Except make it so at zero the opening shows the base of the needle, transitioning to the highest speed where the opening shows the tip of the needle.

Another idea might be to take an Arduino and have it take the input pulses per mile, square it (and divide it as needed to scale it down), and send out the appropriate pulses per mile to the speedo. And have the speedo numbers adjusted accordingly.

The only tough part is that at low mphs, there will be very little accuracy to how fast you are really going, to make up for the huge scale of the larger mphs.

Wouldn't affect the speeds I go anyway. :confused:

A thought that hit me as I read the above post... what about a SG Xgauge that outputs "acceleration" ... this could be a good indicator for hitting that BSFC sweetspot. Am not absolutely sure of the physics, but when accelerating up during a P&G, it could help in looking for that acceleration peak as the throttle pedal is depressed.

I am substituting the dyno by a vehicle at different speeds. So instead of measuring the engine power as heat energy produced by a brake, can we measure acceleration as an indicator of potential energy given into the vehicle mass, to give a similar reading but in a more dyamic setup.

I am leaving my initial thoughts here for anyone with a better understand of the whole thing to take things forward (or debunk my hypothesis!)

In a way, I like this approach because it would be real-world acceleration that would actually factor in rolling friction and aerodynamic drag ...

You can display speed (or whatever) on an analog gauge without carrying a laptop too:
http://ecomodder.com/forum/showthrea...html#post61186

http://opengauge.org/diympggauge/analog/pic8.JPG

Didn't get that the first time I read it. Second time around the light bulb came on - amount of needle you see (from say 20 - 85 mph) is proportional to v². Amount of needle you see from 0 - 20 is fix because v² is so relatively small in that range. Amount of needle you see from 85 - Max mph is fixed because v² becomes so relatively large in that range.

I think this should be completely do-able! Great solution wagonman76. Not sure how valuable this would be, but I may give it a try.

One easy retrofit would be a line along the scale of your speedometer that gets thicker in logrithmatic fashion. You'd still have the precision numbers for staying legal in town, but the width of the line where it intersects the needle gives the power.

To assist in getting a sense of the difference in drag between 53 and 75, just stick your arm out the window.

Not quite that, but something similar. A photo-retouched '99 Escort Speedo with florescent purple lines proportional in length to v².
http://i490.photobucket.com/albums/r...scortGuage.jpg

With regard to the coasting distance, it might. I have a spot on my commute that involves coasting down a hill, then up to a light that I typically have to wait at. If I accelerate to 32 mph, then EOC, I will come up short. 35 and I have enough juice to clutch-start at the stop line just as the light turns green.