The

Rogers

Hardness

Comparator

****** Please, Read this Page! *******

Many people will skip over documentation and try to work mostly from the pictures. You can probably do that with this project and still get fair results but there are a few things you should know about.

This document is designed so that you can read straight through it and build the machine step by step. That provides a process which is transparent to the reader that helps you put the three support beams in their proper places (you'll notice that none of the pictures have precise locations specified for these supports). Consider that, if you intend to work by pictures alone.

Many places in the documentation I use the words center and exactly in italics. This is to draw your attention that the measurement is from the center of a hole or that a measurement should be done very carefully. But, despite that emphasis don't over do it. The measurements could be off by as much as 1/16 " or more without doing too much damage.

Horizontal beams are shown in orange and vertical supports are in blue in the illustrations. The illustrations are not drawn to scale.

On page 10 there is an important warning. So that you don't miss it, I'll quote part of it here:

With the Load Beam in the upright position you have, in effect, a very large sledge hammer waiting to fall. If this beam should fall unexpectedly the best you could hope for is that the machine will be ruined. In the worse case scenario, such an event could be fatal if someone were sitting in front of it at the time as might be done when operating the machine (not the recommended position!). So, do not skimp on this safety!

The safety mentioned at the end of the paragraph is a piece of steel that prevents the Load Beam from coming down when it isn't supposed to. Don't overlook this piece in the pictures or think that it is unimportant! It is VERY important!

Another warning: don't put anything on the anvil that you don't want to crush! Even without the penetrator the machine still provides about 500 psi of crushing force.

There are a few photographs of the prototype machine that you may find useful on my website at www.rayrogers.com/rhc.htm

If you have questions or comments regarding this machine, email them to me at rhc@rayrogers.com

Table of Contents

Section Page

Operational Concept 1

Constructing the Base 1

Anvil and Support Layout 3

The Pre-Load Support 4

The Pre-Load Beam 5

The Load Beam 9

Safety Lock Warning! 10

The Gauge Beam 11

The Gauge Base 15

The Weight 16

Casting Lead Weights 17

Attaching the Weight 20

Final Assembly 21

Initial Adjustments 21

How To Use The Machine 23

Hints 26

The Rogers Hardness Comparator

Operational Concept

The hardness testers that would normally be available to the average knife maker generally sell for $700 to $4000 for the stationary models. All of these machines that I have seen work on the same basic principle: apply a lot of force to a diamond point and measure how far it can be forced into the material being tested. When you are talking about hardened blade steel in the Rc 60 hardness range that is not very much penetration at all. In fact, it's just a tiny little dimple. To make things more difficult, the depth of the dimple in a Rc 60 blade is scarcely any different than the dimple in a Rc 59 or Rc 61 blade. Therefore, you will find that, even with the expensive commercial machines, getting an accurate determination of the hardness of a blade is a technological art. It takes skill, it takes practice, and it requires absolute consistency and repeatability of the process both from the machine and from the operator.

In order for the machine to achieve the needed consistency of operation it must be as rigid as possible. This is why the commercial machines weigh about 150 pounds or more and why nearly all that weight is in the frame. The internal mechanism is actually quite simple. The gauge that displays the hardness is the exception to the simplicity of the commercial hardness tester and the part that gives us the most challenge to duplicate. The commercial units have custom built gages designed specifically for that purpose. Since we do not have these gages available to us we must make do with a commonly available unit. That restriction puts the requirement of consistency and repeatability very squarely on both the machine we will build and on the operator. Think of learning to use this device as similar to learning to grind a blade free hand. It will seem difficult at first but, with practice, you will learn the art.

Constructing the Base

The minimum dimensions for the Base are 16.5" x 10". It should be as thick a piece of steel as you can find so as to provide as much stability and rigidity as possible, with 3/8ths inch being the minimum thickness. If you have a larger piece that can be used, that would be even better.

If you don't want to buy a solid sheet of steel for the Base there is an alternative method for providing a Base. The Base can be welded up from bars of mild steel assembled into the shape shown in the picture below:

The bars in the picture are intended to be 2" wide. You would need about 6 feet of 2" wide bar. If you have to buy it, the cost will be nearly as much as a solid sheet and you would still have to weld it and get it flat.

Wider bars could be used, and narrower bars could be used as long as they cover the same areas as these bars. Again, the thicker and heavier the bars are the better the result will be. The Base should be as flat as possible, especially on the bottom side, in order to make the most solid contact possible with the table. In operation, there will be considerable force pulling on this Base in ways that will try to make it flex into the shape of a taco. Your task here is to build a Base that will not flex when bolted to a heavy table. Any flex in the system will skew the machine's ability to measure the difference between the depths of the dimples described earlier.

Anvil and Support Layout

Here are the relative locations of the beam supports and the anvil:

The beam supports are made from 1" square solid steel bar. Using anything smaller than 1" square would not be advisable. The Gauge Beam support will be made from 3/8" steel bar. All the supports will be welded as perfectly perpendicular to the Base as possible. Dimensions for the exact placement of the supports are provided later.

The anvil will be the first part that gets attached to the Base. The dimensions of the anvil may be adjusted to suit the size of the knives you most likely will be testing. As you can see, the Pre-load Beam support is mounted at the edge of the Base. The anvil will need to be sized and positioned such that the part of the anvil that will support the area of your blade where the penetrator will make contact is exactly 2.5" from the center of the Pre-Load support.

The anvil may be made from any steel and it may be hardened or not. It must be as inflexible as possible which is why a thickness of 3/4" is recommended. On the prototype, the anvil measured 1.5" wide by 4" long and was centered at 2.5" from the center of the Pre-Load support.

At this time, the anvil should be attached to the Base. If you decide that you will need anvils of different shapes for different applications the anvil could be bolted to the Base. In this case, be sure that the bottom of the anvil mates perfectly with the Base. Otherwise, weld the anvil to the Base and then take the Base to a surface grinder and level the face of the anvil. The requirement of surface grinding the anvil while attached to the Base is the reason you do not want to mount any of the supports before the anvil is finished.

Grinding the face of the anvil, and perhaps, grinding the Base to make it perfectly flat if you decide that is necessary, are the only surface grinding operations needed for this project. If you do not own a surface grinder these jobs could be done by a local machine shop.

Cover the face of the anvil with a piece of cardboard and tape it in place. This will prevent welding spatter from marking the face.

The Pre-Load Support

This picture shows the various support beams and indicates the height of the center of the pivot hole in each beam. As long as you get the center of the pivot hole within 1/4" on the two main beams and 1/8" on the Gauge Beam that should be good enough.

Notice how the front side of the Pre-Load Beam Support is radiused around the pivot hole. This allows the Pre-Load Beam to fit closely without binding. Mount the beam so that it faces the anvil squarely and at a distance that puts the center of the pivot hole exactly 2.5" from the spot on the anvil where you want the penetrator to

touch (this would generally be on the centerline of the anvil).

The pivot hole in the support beam is 1/2" in diameter and must be very precisely fitted to the pivot pin which will be made from 1/2" drill rod. Drill the hole undersized and ream it to 1/2". Now would also be a good time to cut a 2" section of the 1/2" drill rod to make the pivot pin. It will be easier to fit the pin to the pivot hole before the support is mounted to the Base. Any method you have available to secure the pin in place when it is in use would be fine. Cotter pins were used on the prototype but E clips or clevis pins or even a screw tapped into the side of the pin would do.

After the pivot hole and pin are fitted together, mount the Pre-Load Beam to the Base.

The Pre-Load Beam

Before continuing, let's take a moment to look at how the two main beams work together. In the picture below, you can see how the Load Beam will cross over the Pre-Load Beam. Notice that both beams are close to the outside edges of the Base and the Load beam has a large weight on its end. This arrangement would cause the machine to tip over when in use and that is one reason for the heavy Base and also why the Base must be secured to the table it rests upon.

The next step is to build the Pre-Load Beam. We will build it now so that, if there is any slight variance in the pivot that allows the beam to lay slightly off center, we can adjust for that when the support for the Load Beam is positioned. It is more important that the two beams contact each other correctly and cross at the proper location than it is to have them meet at a precise 90 degree angle (although that is preferred).

Start by cutting an 18" section of your 1" square solid steel bar. In the picture above you can see that the beams have a piece of metal welded to either side forming a tie-rod style of connection. Since the beam and the support are made from the same bar, and the tie-rod ends are flat against the side of the beam, a very close fit should result. Make the tie-rod pieces of 3/16" steel (or heavier) and leave them longer than they need to be. This will allow you some room to drill the pivot holes in a position that will not bind with the support. The exact position of the pivot holes in the tie-rod parts is not critical but try to keep them as short as possible to reduce flex in the system. Also, have at least one square inch of the tie-rod pieces welded against the side of each beam.

Right now, the important thing is that the beam swings smoothly on the pivot. If there is any lateral play in the pivot you can make a washer to reduce it. In order for the beams to contact each other at precisely the same point every time (necessary for the consistency discussed earlier) lateral play must be minimal. However, it is equally important that the beam moves smoothly and does not bind.

Drill and tap the hole that will hold the Penetrator Assembly. The center of this hole should be exactly 2 1/2" from the center of the pivot hole. Use the size Q drill bit and tap the hole with the 3/8 - 24 tap if you are using the recommended 3/8 - 24 all thread. Do not use anything smaller than 3/8ths for this part. Dill and tap for the set screw also at this time. Do not install the set screw, the bubble level, or build the Penetrator assembly just yet as they could be easily damaged.

Notice the green tab that is attached to the underside of the Pre-Load Beam. This tab may be made from 1/8" or thicker steel. It is 3/4" wide and 2" in length. The tab is centered under the Pre-Load beam so that 1/2" of the tab protrudes from each side. Weld this tab in position 14" from the center of the pivot hole.

When not in use, the Pre-Load Beam is supported by a spring loaded stand, as seen in the picture below:

The stand is made from a section of 1/4" or larger rod. The rod is bent into a sort of C shape of the dimensions shown. These dimensions do not have to be perfect. A small screw (4-40 or larger) can be tapped into the side of the stand to act as an anchor for the spring. The short piece (1.5" ) of the stand will pass through a clearance hole in the beam and can be secured by a cotter pin, E clip, clevis pin or other such method. When you are ready to use the device you will lift the beam and the spring will retract the stand. The spring needs to be sufficient to lift the stand so that it stays clear of the Base when the beam is in a horizontal position.

The location of the anchor for the other end of the spring will be determined by the length and strength of the spring you are using.

Drill a clearance hole for the top of the stand to pass through the Pre-Load Beam at a point 13.5" from the center of the pivot. Notice how the stand is intended to rest against the left side of the tab. This picture is not to scale.

The weight will be added later. Putting the weight on now would only make the beam more difficult to handle.

The Load Beam

Construction of the Load Beam begins the same way as the Pre-Load Beam. Start with an 18" section of the 1" square bar, add the tie-rod connectors and drill them for the pivot pin. Then, drill and tap the hole for the 3/8-24 all thread exactly 2.5" from the center of the pivot hole. Drill and tap for the set screw also.

******IMPORTANT! Read this Paragraph! *****

The picture above illustrates the Load Beam and shows that it appears very similar to the Pre-Load beam. There are two important differences: there is no penetrator on the screw and a safety lock has been added near the pivot. The Pre-Load beam has its stand to rest on when the machine is not in use but the Load Beam will probably be in the upright position at that time. Because this machine requires a considerable amount of table space having the Load Beam down all the time may be inconvenient. Also, the Load Beam exerts substantial force on the Pre-Load Beam and the stand may not be able to support it. With the Load Beam in the upright position you have, in effect, a very large sledge hammer waiting to fall. If this beam should fall unexpectedly the best you could hope for is that the machine will be ruined. In the worse case scenario, such an event could be fatal if someone were sitting in front of it at the time as might be done when operating the machine (not the recommended position!). So, do not skimp on this safety!

The safety is made from 1/4" (minimum) steel. Mild steel could be used but the extra effort of using a hardenable steel and tempering it to spring hardness is justifiable. Make the safety 1" wide and 3.5" long or longer. This next picture shows the lock from the side view:

Notice that there is also a tab welded to the back of the beam to prevent it from falling over backwards. A piece of mild steel 3/16" or more in thickness and around 3" long should be fine for this part.

Drill a clearance hole for the safety's bolt so that the center of the bolt hole is 1.5" from the center of the pivot hole. Of course, they are 90 degrees apart since they are

on adjacent faces of the beam. Run the bolt through the safety and the beam and secure it using a nut with a nylon insert so that the safety is able to move freely. Use at least a 1/4" high strength bolt.

Cut a 4.5" section of the 3/8-24 all thread and thread it through the Load Beam. You can attach a knob to the piece if you wish or weld a T across the top. The end that will contact the Pre-Load Beam should be dressed smooth and as flat as possible.

Next, make the support for the Load Beam. This support is exactly like the one you made for the Pre-Load Beam except that it measures 6" from the Base to the center of the pivot hole. Make a pivot pin and attach the support to the Load Beam.

With the Pre-Load Beam mounted on the Base, release the stand and use some wood blocks to prop the beam into a horizontal position. Use one of the bubble levels to get the Pre-Load Beam level. Mark a point on the top of the Pre-Load Beam exactly 16" from the center of the pivot. This is where you want the 3/8-24 screw on the Load Beam to contact the Pre-Load Beam.

You may want to get someone to help with this next step unless you have four hands. Arrange the Load Beam and its attached support so that, when the Load Beam is also in a horizontal position, the contact screw touches your mark in the middle of the Pre-Load Beam. At this time, both beams should be horizontal and they should cross at a 90 degree angle and the Load Beam support should be perfectly vertical and square to the Base. Mark the position of the Load Beam support on the Base. Take the Load Beam off its support and weld the support to the Base.

As with the Pre-Load Beam, the Load Beam should move smoothly up and down with no binding and as much of the lateral play as possible should be shimmed out with washers.

The Gauge Beam

Now we come to the delicate work. Instead of substantial, massive beams we now have to build a small delicate assembly. The purpose of the Gauge Beam is to magnify the amount of movement made by the penetrator so that the relatively coarse gauge that we have can register enough variance between the depths of the dimples to provide us with useful information.

(C) 2004 Ray Rogers Handcrafted Knives All rights reserved
This is accomplished by setting up a Class I lever system ( a see-saw) between the Pre-Load Beam and the gauge that reads the movement of the beam. This is what it looks like:

Here's how it works: the follower rod at the left end of the beam contacts the tab attached to the Pre-Load Beam. This is the other side of the tab that also serves as a stop for the stand on the Pre-Load Beam. The gauge's contact point rides on top of the big screw head at the other end of the Gauge Beam. When the Pre-Load Beam is not bearing on a blade - such as in the brief time between consecutive tests - the spring mechanism in the middle of the picture maintains pressure against the gauge's contact point and thus helps insure consistent consecutive readings.

Here is a view of the mechanism from the rear:

The support beam is made from 3/8" square steel bar. This same bar can be used for the lower beam that forms the support for the spring mechanism. If at all possible, a 3/8" square aluminum bar should be used for the Gauge Beam itself. It is very important that this beam be as rigid as possible but it should also be as light weight as possible.

Unlike the first two beams, the Gauge Beam support has the tie-rod ends attached to it rather than to the beam itself. There is no substantial force applied to this assembly so strength is not a big issue. Smooth operation, on the other hand, is extremely important. In effect, you are building part of the gauge itself. There are ways to build a pivot that will work with less drag than this one but they are more demanding to make and more delicate. This will work fine as long as it has a smooth action.

Weld the tie-rod ends to a section of the 3/8 square stock. Before cutting it to length and before you drill the pivot holes in it, cut the material for the Gauge Beam. Note that the Gauge Beam is not 6" long as a casual glance at the pictures above might suggest. There is exactly 6" between the center of the follower rod and the center of the contact point screw so the beam is a bit longer than that. Cut 7" to start with.

The first step is to drill a hole for the follower pin. This pin is 1/8" hardenable steel, stainless or carbon doesn't matter but it should be hardened. Drill the hole undersized and ream it for a close clearance fit. The pin should be able to move through the hole smoothly without being forced. The gray dot adjacent to the pin in the picture is a set screw. Any small screw will do, so drill and tap this hole too.

Now that you have the follower pin hole near one end of the Gauge Beam, measure exactly 1" from the center of the follower pin hole and mark the location for the pivot pin on the adjacent face of the beam. A 1/8th pin is fine for this pivot so, again, drill undersized and ream for a close but non-binding fit (a #30 ream is a good match for a 1/8 pivot). From the center of the pivot hole measure exactly 5" to the other end of the beam and mark the location of the center of the contact point screw. A 10-32 screw is a good size for this purpose but other sizes would do as well. Drill and tap for the screw you plan to use.

The screw you use should be fully threaded, have a flat head, and be about 1.5" in length. Make a small disk about 5/8" in diameter of some thin sheet metal and weld, braze, or solder it to the top of your screw. Dress the top of the disk as smooth, flat, and square to the threaded section as you can make it. Making the disk highly polished is desirable. Drill and tap for a set screw for this hole as well. Trim off any excess length from both ends of the beam.

Mount the Gauge Beam to its support. Drill the holes in the tie-rod pieces far enough from the end of the support to allow the Gauge Beam to travel at least 30 degrees from horizontal. Like we did before, we will want to shim out any later slop before we're done. Cut the support so that it measures 2 7/8" from the center of the pivot hole to its Base.

(C) 2004 Ray Rogers Handcrafted Knives All rights reserved
Next, cut a piece of the 3/8" square steel bar that is about 2" in length. As close to one end as is practical, drill a hole about 1/4" in diameter. This hole needs to be large enough to create a sloppy fit for a 1/8" rod but small enough so that the spring you are using cannot slip through it. Weld this piece to the support so that the bottom of this piece is 5/8" from the bottom of the support and so that the center of the hole is 1.5" from the back of the support. These measurements are in the pictures above if you need clarification.

Take a 5" long piece of 1/8" steel rod and put a very sharp 90 degree bend in it about 1.5" from one end. This angle cannot be a gentle bend, it must be sharp at 90 degrees and the two legs must remain straight. Once this is done, cut the legs so that one measures 1" and the other measures 2 5/8" as shown in the illustration above.

With the Gauge Beam and its support laying on the table and set at 90 degrees to each other put the bent 1/8" rod through the big hole you drilled in the lower support. Set the rod near the center of this hole and parallel to the Gauge Beam's main support. Mark the location on the Gauge Beam where the short leg of this rod is to pass through. Drill and ream that hole for a close clearance fit.

The final part to be made for the Gauge Beam assembly is simply a short section of 3/8" rod, preferably aluminum but steel will do. A 3/8" to 1/2" length of 3/8" diameter rod with a hole drilled through the center is all this part is. The hole will be a close clearance fit to the 1/8th rod. Put a set screw in it so that this part is adjustable along the length of the rod.

In order to add this new part to the Gauge Beam assembly you must remove the Gauge Beam from the support. Put the short end of the 1/8" rod through its hole in the Gauge Beam, slip the spring over the other end of the rod, and lower that end of the rod through the hole in its support bar while setting the Gauge Beam into the tie-rod ends at the same time. Once assembled, there is no need to secure either end of this 1/8" rod as the fit is too close to allow it to escape.

Finally, adjust the spring so that the Gauge Beam is held at 90 degrees to its support beam. Place the Gauge Beam support on the Base so that the follower rod is well centered under its side of the tab on the Pre-Load Beam (which is again perfectly horizontal) and the Gauge Beam support is square to the Base. Mark the position of the Gauge Beam support on the Base.

Disassemble the Gauge Beam assembly and weld the Gauge Beam support to the Base.

(C) 2004 Ray Rogers Handcrafted Knives All rights reserved
The Gauge Base

The final piece to be mounted on the Base is the Gauge Base. The normal magnetic base that you acquired for this project could be used by simply clamping the magnet to the Base. This would work fine as long as the magnetic base were never moved. It would still work after being moved but it is unlikely that the exact numbers you got when you calibrated your machine could be reproduced. So, in the cause of consistency a permanent support for the gauge is recommended.

You have seen the approximate location of the Gauge Base in the earlier illustrations. In this next illustration you see how the gauge is to be mounted in relation to the Gauge Beam assembly:

The Gauge Base used on the prototype was simply a 1" cube of steel welded to the Base. The threads on the gauge's support beam that originally screwed into the magnetic base were metric threads. Rather than acquire the matching metric drill and tap, a clearance hole was drilled in the steel block and filled with a very strong epoxy. The gauge's support beam is held very securely that way. The Gauge Base can be welded to the main Base anywhere that allows the gauge's face to point in a convenient direction for you to read it when using the machine. Of course, it goes without saying that the Gauge Base should be welded to the Base before the epoxy is used.

Penetrator Assembly

Cut a 4" section of the 3/8-24 all thread. Put a knob on one end and secure it with a jam nut (or weld a cross bar if you prefer that to a knob). Next, cut a 1" length of 3/4" round bar. 3/4" drill rod was used in the prototype but most anything that could be used to make a pommel on a knife could be used for this piece.

(C) 2004 Ray Rogers Handcrafted Knives All rights reserved
It is important that the face of this piece that will accept the penetrator be as flat and square to the centerline of the part as possible. Drill a size C hole lengthwise through the centerline all the way through the piece. Ream it with an 1/4" ream. Now, drill a size Q hole from one end and centered on the 1/4" sized hole. Drill the Q hole no more than 1/2" deep. Tap the Q hole for 3/8-24. Drill and tap a hole for a 10-32 set screw in the 1/4" sized portion of the piece. Finally, assemble the parts so that they look like this:

Do not leave the penetrator in the assembly at this time. Also, never let the penetrator touch the face of the anvil. That would cause a dimple and make the surface uneven.

The Weight

The final phase of major construction will be making and attaching the weight. The weight can be round, square or rectangular. It can be long and thin or short and fat. It can be made from steel, lead, or a combination of both. It can be welded to the beam or attached with a bolt. But, however it is made and attached, it should adhere very closely to the specified weight and be attached at the specified location. A small variance here can make a significant difference in the performance of the machine. In all honesty, a small variation might improve the performance in some cases. Several variations were tried on the prototype and some were clearly more effective than others.

Some simple arithmetic will be required to determine the proper length for the weight when made from commonly available bars or rods. The object of the game is to make the weight weigh between 10 and 10.4 pounds . Do NOT try to use a scale to weigh the weight to avoid doing the calculations unless you are certain the scale is accurate in this weight range. A bathroom scale will not be accurate enough.

Examples of the calculations for most of the likely options are listed below.

Steel Weights

The simplest weights to make are solid steel weights. The supplier listed for steel on the Supply List will cut any size solid steel rod or bar to any length you specify, so, find out what is available in about a 3" or larger thickness and use that thickness in the following formulas to figure the length required:

Formula for round rods: Length = 11.46 / ((Diameter x Diameter) / 4)

Example: Let's say the supplier has some 3.25" diameter rod available.

Diameter x Diameter is 3.25 x 3.25 = 10.56

10.56 / 4 = 2.64

Length of the large weight is 11.46 / 2.64 = 4.34"

******

For solid square or rectangular bar: Length = 36 / (S1 x S2)

S1 and S2 are the lengths of the sides of the square or rectangular bar. For a square bar S1 and S2 would be the same value.

Example: Available rectangular bar measures 2.25 x 3"

S1 x S2 = 2.25 x 3 = 6.75

Length of the large weight is 36 / 6.75 = 5.33"

Casting Lead Weights

If you will be casting lead weights using a sand mold or any other disposable form that results in a plain lead weight without a casing you will you will probably want to cast the lead around a bolt so that the weight can be attached to its beam. Make sure the bolt is dead center in the face of the weight. The weight of the bolt can be ignored.

For easy reference, the formulas would be:

Square or rectangle: Length = 24.4 / (Side1 x Side2)

Cylinders : Length = 24.4 / (3.14 x Radius x Radius)

Example: The length for a 2.5" square lead weight would be :

3.9" long for the large weight = 24.4 / (2.5 x 2.5)

The length for a 2.5" diameter cylindrical lead weight would be:

5" long for the large weight = 24.4 / (3.14 x 1.25 x 1.25)

*********

If you will be casting your lead into a casing things become a little more complicated because the weight of the casing must be taken into account. It will be assumed that the casing is made of either square, rectangular, or cylindrical steel tubing. The following information will not be accurate if anything other than steel tubing is used.

What we need to do is shorten the steel case so that it holds less lead by an amount that weighs the same as the remainder of the steel casing. Here then is the process:

The first step is to figure how long the casing should be using the formulas for the caseless weights above. Let's assume you want to use a piece of square tubing that measures 2.5" on each side of the interior. That's the same size we used in the caseless example above so we already know that the calculation will tell us the length should be 3.9". But, using 3.9" of steel casing will add the weight of that casing to the already proper weight of lead.

Let's assume further that your casing has a wall thickness of 1/16". This is enough to make a significant difference in the weight and any thicker wall would be even more significant so don't give up on this process.

Now, we need to know the volume of the exterior of the steel case. If the walls are 1/16" thick, then the length of the outer sides would be 2.5" + 1/16" + 1/16" = 2.625"

Formula: Side1 x Side2 x Length = Volume we'll call this V

Example: 2.625" x 2.625"x 3.9" = 26.87 = V

Next, the weight of that much steel:

Formula: (V - 24.4) x .28 = W gives W, the weight of the casing

Example: (26.87 - 24.4 ) x .28 = .69 24.4 is a constant

How much lead would weigh the same as that much steel:

Formula: W / .41 = VL VL is the volume of lead

Example: .69 / .41 = 1.7 .41 is a constant

Finally, what length of case this size would hold VL :

Formula: VL / (S1 x S2) = L S1 & S2 are the interior side lengths

Example: 1.7 / (2.5 x 2.5) = .272 "

So, in this example, we would shorten the case by .272" and reduce the original 3.9" to 3.63" Obviously, no one expects you to be able to cut the tubing that precisely but getting as close as you can will significantly reduce the .69 pound of over weight and bring it into a more acceptable range.

*********

For cylindrical tubing the same basic process applies. Starting with the formulas for the caseless lead weights and using the caseless example of cylindrical tubing with a 2.5" diameter interior, we know that the length of the tubing should be 5" for the large weight. Let's again assume that the wall thickness is 1/16". The diameter of the outside would be 2.625" and the radius would be half of that, 1.31"

To get the volume of the outside of the casing:

Formula: 3.14 x Radius x Radius x L = Vo Vo is Volume of the outside

Example: 3.14 x 1.31 x 1.31 x 5 = 27.05 3.14 is Pi, a constant

The volume of the casing itself would be:

Formula: Vo - Constant = Vc Vc is volume of the casing

Example: 27.05 - 24.4 = 2.65 24.4 is a constant

The weight of that much casing would be:

Formula: Vc x .28 = Wc Wc is weight of the casing

Example: 2.65 x .28 = .74

The amount of lead that would equal the weight of the casing:

Formula: Wc / .41 = VL VL is volume of lead

Example: .74 / .41 = 1.80 .41 is a constant

And finally, the length by which the tubing should be shortened:

Formula: VL / (3.14 x Radius x Radius) = L L is length to shorten

Example: 1.80 / (3.14 x 1.31 x 1.31) = .33 3.14 is Pi, a constant

In this example then, the length of the cylindrical tubing would be shortened by .33" which would make it 4.67" instead of 5" in length thus reducing the weight by .74 pounds.

NOTE: To avoid the inevitable emails that come when someone writes something as complex as this, let me say ahead of time that I am aware that these calculations are not precisely accurate. The volume of the steel removed from the casings is treated as though it weighs the same as an equal volume of lead. Of course, it does not but the difference is not considered significant and is ignored in an effort to keep this as simple as possible.

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Attaching the Weight

This picture shows the two ways the weight might be attached to the Load Beam:

Originally, you cut both beams to a length of 18". After that, the tie-rod ends were added which increased the length. If you will be welding the weight to the Load Beam first trim the beam's length back to 18" as measured from the center line of the pivot. Then put the end of the beam on the center line of the weight and weld it in place.

If you will be using a bolt, drill the hole for the bolt in the beam so that the center of the bolt hole is 18" from the center of the pivot. Trim off as much of the excess length on the beam as is practical.

At this time, you should also shorten the Pre-Load Beam so that it also measures 18" from the end of the beam to the center line of the pivot.