### Breaking the law

I think that you made a small but common mistake in your answer to the February Fun with Fundamentals puzzle. While the Ideal Gas Law is commonly used by first-year chemistry students, a better approximation uses the ratio of specific heats as an exponent in the equation. Using Charles’ Ideal Gas Law, final pressure for the problem is 3,254 psig. Using specific heats, the final pressure returned is 3,987 psig — making the first answer 18% too low.

*Jim Montgomery**[email protected]*

### Symbols are ‘Greek’ to reader

In “Applying Stepmotors Successfully” (on your Web site), the equation is: J=(¶Lpr^{4})2g: where r is the density of the screw, L is the length, r is the radius, and g is the gravitational constant. Could you please clarify something for me? I’m trying to use this equation to calculate the inertia of the adjusting screw of a regulator. We’re trying to size a stepper motor to actuate the regulator. Another of the articles in this series (Day 1: Torque and inertia) recommends that “load inertia be no more than seven to 10 times that of the rotor.” So, I can get the rotor inertia from the motor spec. My questions are: Is “¶” a typo or some sort of normalization constant? If it’s a constant, what is its value and what are the units?

Also, I assume that “p” is the density of the screw.

*Linda Nistler**Tescom Corp., ECD*

The correct equation (in the March issue of MSD) is: J = π *Lp r ^{4}/2g*. Where π is pi (3.14...), L is the length of the screw,

*p*is the density of the screw,

*r*is the radius, and

*g*is the gravitational constant. In this age of digital printing, sometimes Greek characters do funny things.

*I am also forwarding your question to the author, Allen Chasey. He can verify what I said and take you a lot further toward a solution to what you are trying to do. - Ed.*

### ‘The future don’t work’

Happened to finally get my May issue from the office routing. Certainly some highway improvements and new construction are in order. However, from Los Angeles to Bangkok the historical pattern has been congestion = more roads = more congestion, and so on. Here in the U.S., I would aver that spending vast amounts of tax dollars on road building trying to stay ahead of road congestion will be like chaff in a typhoon due to the inexorable proliferation of urban sprawl.

One master-plan highway expansion leads to another. And without centralized business districts (i.e., real cities), mass transit won’t succeed even if you could lever suburbanites out of the “freedom” of their beloved snarling metallic beasts. Apparently the herd does not mind spending vast amounts of time in increasing gridlock, or deludes itself that another road expansion (but certainly not in their back yard) will alleviate the situation this time.

I’m not sure what the “answer” is, but continuing the existing pattern leads to a paraphrase of some cartoon character, “I’ve seen the future and it don’t work.”

*Glenn Gabryel**[email protected]*

### Prize was overstated

I’m sure you’ve probably already been made aware of this, but I thought I’d mention it anyway. I believe the cash prize awarded by DARPA for the robotic vehicle Grand Challenge race is only $1 million, not $100 million as it stated in Robotic Road Warriors in the August issue of *Motion System Design*.

Cool article though; hope to see some coverage of it on TV somewhere.

*Derek Hoy**[email protected]*

*Thanks, Derek,**You’re right, it’s $1 million. If it were $100 million, Lockheed, General Dynamics, and Ford Motor would probably be lining up to enter. - Ed.*