The Waltz Radius Ruler is a ruler or tool developed by Stanley J. Waltz Jr. and  Bryan F. Bechtol which can actually change the way we measure circle or round objects.

We are not asking or telling you not to learn the formula mathematically, were just making it a whole lot simpler.

This tool/ruler can be used to get the radius of a curve or an arch without using a formula, a formula that still allows for a margin of error.

What’s so great about the Waltz Radius Ruler?

You will not have to have a background in mathematics; you just pull it out of your pocket or toolbox, and measure the radius in seconds.

If we get this in the Common Core Standards, it will have a significant impact on the future and employees will become more efficient therefore they will save time and money.

We have made the Waltz Radius Ruler Free to all teachers and students by putting it on Facebook or simply login to our website for complete instructions.

Copy, Paste, Print and build your own for free!

If you wish to purchase a plastic Waltz Radius Ruler please feel free to order one from our website.

The Waltz Radius Ruler will become available for purchase in May 2016.

The Radius Ruler: Measuring the Neglected Dimension

By: Stan Waltz Jr. - B.S. in Physics - E.W.U. “89”

I invented a new measuring device so simple it only has 1 moving part, and is so basic in utility that its applications will likely reach into every major sector of industry, yet it was somehow overlooked until now. The basic design of the radius ruler allows the user to measure the radius of a curve with a minimum 60° arc, with caliper accuracy, and a standard reading range of up to 12” (2”, 4”, 6”, 8”, or 12”),. The patent (# 7497027 at the U.S. patent office) allows for flexibility in design to customize tools for a wide range of special applications.

We have tools for measuring a length, or an angle, but nothing for measuring the radius of a curve. For all intents and purposes, the radius of a curve always had to be determined. For something like a circle where the arc is greater than or equal to 180°, the radius is easily and accurately determined by taking half of the measured diameter.

As we try to determine the radius of arcs less than 180°, the situation changes significantly.

Pre-cut arcs can be used like “feeler gauges” to estimate the radius, but accuracy is limited by the size of the arc increments. The set with the most accurate increments of .015” only goes up to 1”. Some sort of graphic solution can be used by first locating the center of the radius of curvature, and then measure from there to the curve. Accuracy can be compromised by both the ability to physically locate the center of the radius of curvature, and by how accurately the distance from that point to the curve can be measured.

Three points can be used to define a curve, and this is the basis for how a group of inventions work, including mine. This approach allows the radius to be measured directly.

It takes 3 points to define a curve of radius (R). Two of those points can be located by placing the curve in a fixed “V” of angle alpha (α), and the angle gamma (γ) between those two points represents the amount of arc required to measure the radius, and γ is a function of α as shown in fig. 1. Note the inverse relationship between these two angles, in that γ decreases as α increases. The third point is established by aprobe measuring the distance from the base of the “V” to the curve (H).

When α = 60°, γ = 120°, and H = R.

Most of the inventions using this approach require α =60°, but that requires an arc (γ) of 120° to measure the radius, meaning you couldn’t use it to measure the rounded corners of a rectangle (γ =90°). Figure 2 shows how increasing α effectively compresses H, meaning the probe measuring H would require a greater sensitivity to achieve a comparable level of accuracy. I do this by using a wedge to gauge the radius R, as seen in figure 3. As H is compressed for α greater than 60°, it’s compensated for by decreasing β for the wedge. There is a point of diminishing returns where an incremental increase in α isn’t worth the corresponding loss in β, and I take that point to be α =120° (γ =60°).

This is a big deal because it’s so basic. Some problems are most easily addressed in Cartesian coordinates, others in polar coordinates. As “length” and “angle” are to Cartesian coordinates, “radius” and “angle” are to polar coordinates. We’ve long been able to measure length and angle, but not the basic dimension of radius. Most of the time we describe curves in terms of their radius of curvature, because describing an arc in Cartesian coordinates requires trigonometric functions, so the significance of this basic measurement seems obvious. The radius ruler with its one moving part is not complicated, and I was amazed that nobody thought of this sooner.

There’s no pre-established market for this because it’s not an improvement on an old product. Nothing comparable to this has ever existed, so all the applications will be a new approach to old problems.

According to some educators at the University of South Alabama, a cheap version of the radius ruler would be ideal for helping young math students, because they typically have a hard time grasping the concept of radius. One professor said he wished he had this when he taught 7th graders, and used the area of a circle as an example. He said he could tell the students that π is just a number (3.14…), but he’d lose them at R. With this he said he could have passed it around with a few round things, so they could measure the radius for themselves, and gain a hands-on sense of the concept. An informal test of this approach worked surprisingly well.

Consider the Quality Assurance people who are required to certify a product meets all the required specifications, and how often that includes radius requirements, like a part with rounded corners that must fit snugly inside/over another part. Some would find it helpful to be able to measure the size of a pipe when they don’t have access to opposing sides, like a construction crew digging around in the earth to find a particular pipe line. Any business with the occasional client who brings in a device, item, product, etc… (thing) to have at least one copy made, but doesn’t have any drawings, would also find this useful. I’m yet to meet a machinist who doesn’t want one, and I’m told it would be handy in wood working. It may take a few years, but I expect applications will turn up in every industry, as production workers realize how this tool could help them do a better job.

Stanley J. Waltz Jr.
(509) 489-3097

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How I came up with the Radius Ruler – by Stan Waltz Jr.

I was working as a brake press operator at a precession sheet-metal fabrication shop. I wanted to branch out into doing some design and layout work, and I noticed how it typically took several tries for the engineers to design a flat pattern for a part that will be in tolerance after it’s formed. I thought that we should be able to get it right the first time (at least most of the time), so I decided to take a closer look at how metal bends.

For a bend in a piece of metal, the metal on the outside of the bend is in tension from being stretched, and the metal on the inside of the bend is compressed. Somewhere in the thickness of the metal, the portion in tension meets the portion in compression, and between them is an un-stressed line that isn’t stretched or compressed. I needed to know where that line was.

It seemed obvious that an empirical approach would yield the most accurate solution, because it would be based on physically bending test pieces of metal, as opposed to being based on the theoretical projections of some mathematical model. It takes careful measurements, from before and after each test piece is bent, to develop a data base. If done properly, it would only need to be done once, and it would establish a standard of accuracy that the mathematical models could be judged against.

Initially I tried to use an angle measurement, with a combination of length measurements, to analyze the test bends. More length measurements can be made on a test piece than the minimum necessary to solve the problem, but the calculated result varied significantly depending on which combination of length measurements I used. It became readily apparent that I could get much more reliable results if I could accurately determine the resulting bend radius, but I couldn’t.

I came to realize that I needed to be able to measure the radius of a 60° bend, with sufficient accuracy, and a reading range larger than 3 inches. I checked the tool catalogs, and our regular suppliers, and there was nothing that would come close to working. I searched the U.S. patent web site to find out what kind of tool I was looking for, but there was nothing there. I started looking at the other inventions for measuring the radius, and thinking about how and why they all fell short. I liked the idea of using a fixed “V”, but the scale compression from using a larger angle for the “V” was a real problem (see fig. 2). One night I was lying in bed thinking about it, and I thought “If only I could feel out the distance from the curve to the base of the “V” with something besides the standard probe”, and then it hit me to use a wedge to feel out that distance (see fig. 3). I designed and made a cheap proto-type for $6 that was accurate to within .010”, could measure up to a 3.5” radius, and only had one moving part (patent # 7497027). It was accurate enough that I was able to develop a data base that got the design and bending operations on the same page. That all but eliminated the need for the extra parts typically required to set up a brake press, and formed proto-types were almost always right the first time.

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            From Cartesian and Polar coordinates and from math generally, it’s clear that some sense of length, angle, and radius are key to students understanding the basic concepts.  Children aren’t born knowing anything about this, and concepts of length, angle, and radius are abstract ideas initially.  They don’t have any sense of inches or degrees, let alone the roundness of a corner called radius.

            Educators found that children learn best when more of their 5 senses are part of the learning process.  They gave students a ruler and protractor, and had them make measurements.  The length measurement required taking the ruler in hand, having to concentrate on using eye-hand coordination to line the ruler up with the thing to be measured, and then interpret the graduated scale on the ruler to read the measurement.  The hands-on experience from making the length measurements gives them the experience required to develop a sense of length.  The same is true with using a protractor for making angle measurements to develop a sense of angle.  The significant benefit from this approach is well known.

            Although greatly improved, children still struggle with the basic concepts because they still struggle with the concept of radius.  Like the 3 legs of a stool, understanding math requires some sense of all three of these basics (length, angle, and radius).  Children still struggle because there wasn’t anything comparable to the ruler and protractor for that hands-on experience with radius (until now).  This basic innovation means students can now get the significant benefit from using a radius ruler for making radius measurements to develop a sense of radius.

            We know from talking to some educators we are right about the benefit of this to students.  This is an American innovation that will be manufactured only in America.  We want to bring this to American students to give them a leg up in understanding the basics of math.  The educational version will be made from thick paper like what we sent you, and this form is accurate enough for teaching purposes, but cheap enough to make sure every student can benefit from it.

            Any help you could give us, weather by pointing us in the right direction, suggesting people/groups we should contact, or anything else to aid in this pursuit would be greatly appreciated.