Speedometer Error Q and Basic Physics Q

Many hand held GPSs do MPH via triangulation. Perhaps you have a friend with one.

Technical Correspondence - Car News - Road and Track
(I suspect being a hybrid changes some parts of this advice)

When I was young and dinosaurs roamed the earth, cars had carburetors, and the typical response to hard acceleration was to pump excess gas into the air flow to avoid lean conditions, so gentle was more frugal than brisk. With fuel injection this is less true. So your father may have been right, once upon a time. (Or he learned it from his dad, who was right way back when)

Carburetor - Wikipedia, the free encyclopedia

 

1. My Gen II speedometer reads 1 mph fast at speeds from 20 mph to 70 mph. I have not tested it a lower or higher speeds. Note that I do not have the factory OEM tires.

2. Ignoring the increased aerodynamic drag caused by faster speeds, classical physics shows that for a given speed, exactly the same amount of work is expended no matter what the acceleration. This means that any difference in energy comes from efficiency, not the physics of speed. For best mileage, you want to accelerate at a rate the runs your ICE at its most efficient. With a Prius, this calls for fairly brisk acceleration, but avoiding WOT and drawing from the battery.

Tom

 

1. Speedo cal will vary by vehicle, and change over the life of tires, maybe even slightly by inflation/temperature. You really need to find a friend with a GPS to get you an accurate number for your car.

2. As others have indicated you are right to the first order. All things being equal, it doesn't matter. The problem is all things aren't equal. The efficiency of the gas engine varies with throttle position. Its generally very inefficient near 0 throttle, hits peak efficiency in the range of 50-75% and then heads south again as you move towards WOT.

I'm an electrical guy, so I don't pretend to understand the intricacies, but here's how I think of it. In a traditional car, the extreme case of low efficiency is sitting with the car idling but not moving. The engine is burning gas just to keep itself running (overcoming its internal loses and friction), but no work is being done. You can get a sense for how much energy is being wasted by how quickly an idling car warms up in the winter, harvesting a small amount of that energy that's being wasted as heat to do something useful. Now the Prius mostly avoids this worst case by shutting the engine off at idle, but moving away from the extreme imagine a case of gentle acceleration. Now at least some of the engines power is being used to push the car forward and increase its speed, but the engine still has to overcome the same losses. In fact the loses probably get worse, since the friction forces are going to increase with speed (rpms in this case). Ideally, accelerating with WOT at low rpms would generally yield the best efficiency since you'd minimize friction by keeping the rpms low, and maximize the ratio of power put to the wheels to that lost overcoming friction and loses. While It hink this may actually be true of some diesels, most gas ICEs have other issues related to air/fuel/exhaust getting in and out of the engine come into play to push the peak efficiency case from WOT back to 50-75% open. The Prius is also complicated a bit by the RPMs and throttle opening both being tied to accelerator position. On the Gen IIs its been recommended to shoot for accelerating such that the instantaneous mpgs equals roughly half your current speed. This puts you in a reasonable band of throttle position and rpms to get decent efficiency.

The same arguments explain why pulse and glide techniques yield better mileage than constant throttle. When cruising, particularly at low speeds, even though rpms are likely to be low so is the effective loading of the engine. Consequently you are often cruising at only 10-20% throttle opening. Overall efficiency can be improved by alternating between say 50% throttle and gliding, particularly in the Prius where the engine will shut completely off during your glide phase. When the engine is on its running at higher efficiency, resulting in more work done for a given amount of fuel burned. It may be my imagination, but I frequently better gas mileage driving up and down hills than at constant speed on flats. My suspicion is that driving up hill increases the loading on the engine, requiring more throttle opening resulting in better efficiency.

 

Ha. Well, I do have some experience with this, of the not-so-good variety.

My wife and I had a 2000 Honda Odyssey. It ran quite fine, etc., but it always seemed like cars were passing me when I was pulling (what I thought) was 70 mph.

So, when going down the Ohio State Turnpike (a flatter piece of soil is hard to find) we timed out a measured mile at 60 mph. Surprise, surprise: We were going 54!

The speedometer read 10% low at all speeds. Brought this to the attention of the Honda folks (car was still under warranty) and they popped up with an official letter stating that speedometers in the U.S. were considered "good" if they were within +-10% of the correct value. And that they weren't going to do anything to fix it.

At a later date got a hand-held GPS. It confirmed our distance-vs-stop-watch tests. I figure, since GPSs are all about time and distance, the GPS has the last word on what the actual speed might be.

We also confirmed that the odometer matched the speedometer. Now my understanding is that there's always some sensor out there marking tire revolutions. That goes directly into the odometer. In ye olden days this was a cable that went from the (usually) front left wheel hub directly into the back of the instrument cluster. (And there's lots of stories about unscrupulous used car dealers, electric drills, and fooling around in the middle of the night.) I imagine this is all done with electric sensors and some extremely-sealed electronics in modern cars.

The speedometer cable used to go into a carefully calibrated mechanical "drag" assembly that would take revolving cable and make the speedometer needle go back and forth in the dash. If the drag was off, I suppose the speedometer and odometer readings wouldn't quite agree.

I don't know from personal knowledge how they do it in modern cars, but, given that I'm a EE in mixed-signal analog design/firmware/DSP coder type of person, I'd imagine that wheel revs vs. some fixed frequency oscillator is how they calculated the MPH.

I have compared the Prius, my wife's Sienna. and a GPS with a speed reading. They're all within +- 1 mph of each other. (After the experience with the Odyssey, I won't leave a car lot without checking the speedometer!).

Now, let's take a look at your equations. I like Physics.

Yep, F=ma, just like Newton said.

V = Vo + at, where Vo is the initial speed. That still works.

Nope, you got the equation for Work wrong. Work is:

W = F * D, where D is Distance. Let's stick with SI units. One Joule of energy is expended when a force of one Newton moves a mass, any mass, exactly one meter. The units of a Joule are, therefore, a Newton-meter.

Let's say we apply a force of one Newton to a kilogram of matter on a frictionless surface. The acceleration will be a = F/m = 1 m/s**2.

The definition of one Joule is the amount of energy that an object acquires when one Newton moves that object one meter. So, to double check, with an acceleration of 1 m/s**2, and distance = (1/2)*a*t**2, at one meter we get t = sqrt(2). (That is, with an acceleration of 1 m/s**2, we go one meter in 1.414 seconds.)

Then, since the energy of a moving object is 1/2*m*v**2, and v = a*t, we get E = (1/2)*1kg*1.414*1.414 = (1/2)*1kg*2 = 1 Joule. Check.

So, back to your original question: What's the difference in energy expended if we go, say, from 0 m/s to 30 m/s (that's 67.1 mph) over one minute (60 s) or five minutes (300 s)?

Easy: It's zero. Since, in both cases, the energy in the moving object is 1/2 * m * v**2.

However, the power required is different. Power is energy per unit time; so, one Joule per second is one Watt. (Yes, and that 100 W light bulb is absorbing 100 Joules of electricity every second..)

So, Edmunds says the Prius weights 3042 lbs, which is 1380 kg. Energy at 30 m/s is 1/2*1380*(30*30) = 621 kJ. Power to get to that level after 60 s = 621/60 = 10.35 kW, or, at 760 W/HP, 13.6HP. Over five minutes, that would be 621/300 = 2.07 kW, or 2.7HP.

Let's see: According to Edmunds, the Prius can generate, at some peak level, 134 HP, or, going back to SI units, 101.8 kW.

So, given that 1380 kg curb mass, assuming no friction anywhere (yeah, right!), we should be able to get to 30 m/s by

621 kG/101.8 kW = 6.1 seconds. Ha.

Reasons why that's not going to happen:
1. Engine and the motor has torque, yes. But power is pretty much (torque * rotational speed), and the rpms of the motors and the engine aren't that good at a dead stop. So, not so much power available at a dead stop.
2. Friction, friction, friction. Friction, both air, tires, and what all is pretty much a non-linear function of vehicle velocity and gets bigger (think I heard a cube factor for air flow, linear for vehicle motion) as the car speeds up. So, it's not just the mass of the car, it's the resistance to motion as the car speeds up.

Lots of fun, but I have to get out of here.

YMMV

KenB

 

Mine is right on compared to GPS but at times it would depend on how each round up or down unless that is a standard protocol to do it at x over whole number to round up.

 

According to a GPS, my speedometer when it reads 60mph it is actually 59mph. Not off by much.

 

Perhaps this is cynical, but having speedometers read faster than reality also reduces the warranty distance liability and gives the false impression of higher MPG. These are better for auto manufacturers than it is for customers. Could it be that manufactures use avoidance of overspeed as an excuse for exaggerating MPG and saving money by reducing their liability for repairs?

 

The speedo on the GEN III overestimates .... but it's the actual Speedometer doing this. The MPH on the CAN BUS (being transmitted to the speedo) is pretty much dead on. (With the stock 15" wheels, at least.)

I can display MPH on my ScanGauge II and see this in action. At 60mph the speedo is showing about 2-3mph fast versus what the car knows the speed is....

It's pretty annoying and it would be great to toggle a setting in the speedo to stop this. I've been poking around but have not found this...

My last car (Mazda Protege) was dead on -- though the RPM gauge on that car was about 350rpm fast at RPM readings above 2000rpm. So when I was hitting an indicated 6500, the ScanGauge II would report only about 6150!

 

Don't take speedometer error as an indicator of odometer error. None of my cars have had matching errors, most didn't even err in the same direction.

While my Prius overreports speed on the display, about the same as many others report here, it very slightly underreports distance, by a few tenths of a percent. My reference is many mileposts on a very long stretch of Interstate highway, where a dozen points scattered along 101 miles were consistent. The next checked posts, between 120 and 130 miles, betrayed a significant survey breakpoint somewhere between the 101 and 120 miles points.

After that class action lawsuit about Honda odometer errors a few years back, I doubt that average odometers are going to over-report mileage anymore.

 

I believe the only way is you get enough political power to modify the "UN-ECE Regulation No. 39".
http://www.unece.org/trans/main/wp29/wp29regs/r039r1e.pdf

Ken@Japan