How to spoke a standard wheel 4 cross pattern
1. Preface
2. How to buy the right components
3. Buying Rims
4. Buying Spokes
5. Familarization with Existing Wheels and Components
6. General Procedure
7. Specific Procedure for 3 cross 36 hole
8. Truing Algorithm
9. References
1. Preface
Review In 2020
I originally wrote this document in about 1990 when I was commuting to the GVRD, about 20 km each way. I had twin Norco 10 speeds I bought used, and the rims had pulled through on both of them, so I bought new rims and rebuilt the wheels. Of course I could have just taped the rim beside the old rim and transferred the spokes, but I wanted to document the process from the ground up. So I sat in the living room night after night and built and rebuilt the same wheel to test and improve the procedure. This was before the internet, so I had it all in a text file. When the internet came out about 1995, I put it on the internet and the Altavista search engine made it the top reference for this subject. Nowdays, many people just buy the whole wheel as one unit (rim,hub and spokes). However many shops still build custom wheels. This is especially useful for bikes with expensive internal gear hubs like Rohloff where you are not going to throw away the whole wheel just because the rim is damaged.
Original Preface: This document will tell you how to get the right components and build your own bicycle wheels. Even if you don't build your own wheels, it will make you much more capable of dealing with existing wheels. The first thing I did to prepare myself to build a wheel was to purchase numerous bicycle maintenance books. However, I found that these books tended to have long, arbitrary methods for lacing and truing a wheel, and that very little theory was explained. Furthermore, none seemed to provide the necessary information to help purchase the right parts. Therefore, I went to various good bicycle stores and wheelbuilders and gathered up the relevent information for myself. The result is this document. It will save you a lot of time talking to bike stores to gather the same information. Even if it is not absolutely complete, it will give you a framework into which you can continue to gather information as the components change in the future. In particular, this document has the following highlights:
The scope of the document is how to buy the right stuff, build an ordinary wheel, and know what you're doing. It does not go into a lot of detail on exotic spoking patterns.
2. How to buy the right components
The key to buying the right components is having a good framework for
analysis of the necessary facts before you talk to the bicycle store.
Before buying a hub, you should clearly understand
1. The measurements that determine dishing
2. The standards that determine the availability of spare parts
It is useful to understand that if the rear hub was wide enough, no dishing would be required. Such a hub would have just as much space on the left as on the right side of the flanges. Thus the flanges would be centered between the dropouts, and the rim would also be centered with equal length spokes, just like the front wheel.
However there is no such rear hub: in general they have much more space on the gear side than on the other side. Therefore, the flanges are not centered, and thus in order to keep the rim centered, the gear side spokes must be more vertical. Because they are more vertical, less of their force pulls sideways, and therefore they have to be much tighter to offset the other side. You can easily verify this by resolving the forces into two perpendicular vectors: one vertical and one side to side. The gear side spokes are typically 2 or 3 times tighter.
The problem with a heavily dished wheel is that only half the spokes are taking most of the load. Therefore all the spoke and rim failures tend to be on the freehub side. It is as if you had an 18 spoke wheel instead of a 36 spoke wheel.
Because of this, one of my main objectives in planning a rear wheel is to minimize the dishing. The need for dishing can be greatly reduced by having wider rear dropouts and putting in larger spacers on the non freehub side to make up the width. In other words, if you increase your rear dropout spacing from 126 mm to 135 mm and put in an extra 9 mm spacer on the left side, you drastically reduce the need for dishing. The dropout spacing can be widened by a bicycle store for 10-20 dollars.
Wider dropouts is also the trend for newer frames. The standard dropout width for racing bikes has increased from 126 mm to 130 mm, and for mountain and touring bikes from 130 to 135.
Shimano hubs tend to have different hub lines aimed at the racing bikes versus the mountain bikes. Eg: Shimano 600 or Deore is aimed at racing bikes whereas Shimano "EX" is aimed at mountain bikes. However, the hubs all have the same "index width", and flange width. To match to any given dropout width, only the axle length and spacer widths need be changed.
Hubs prior to 1992 were intended for 7 speeds, not 8 speed, and thus had narrower freehub bodies, and shorter axles. However the flange width was the same. Such hubs can be adapted for any freehub width by adding more spacers. However, you cannot put an 8 speed cog set on them.
In dealing with any hub from the past, present or future, the following measurements are relevent:
8 Speed 7 Speed ------------------------------------------------ Flange Width 54 54 Index Width 5 5 Freehub Body Length 34 39? Opposite Body length ? ?
The index width is made up of the cog + spacer. The cog is 2 mm and the spacer is 3 mm.
Desired axle length can be varied depending on dropout width. The axle length should be about 3 mm shorter than what you would add up.
135+7+7-3 = 146
130+7+7-3 = 141
125+7+7-3 = 137
3. Buying Rims
A rear wheel rim should be substantially heavier than the corresponding front wheel rim, because it carries double the weight, is subject to torque loading as well as radial loading, and must withstand extra tight spokes due to dishing. Rim failure has been my number one reason for having to build new rear wheels.
To really make an intelligent decision about rims, I suggest you go to a good bike store and get them to make photocopies of the specification comparison sheets from a good manufacturer like Mavic. Then look at the different dimensions on these sheets and form some sort of understanding of each of them.
Before getting into a comparison table, there are several general attributes worth discussing:
Hard Annodizing: Makes the rim surface harder, and thus perhaps makes braking surface not wear out as fast.
36 or 40 holes: 40 Hole is stronger, but harder to get.
Box Section: Are stronger and more expensive than the "wide straight side" standard rim. However, ligher box section rims are more succeptable to rim failure due to eyelets pulling through, or the rim pulling apart. Many quality bikes were built with non-box section rims, and did not have as many rim problems as the box section wheels.
Eyelets: In box section rims, there are some which have only single eyelets, and there are others which have double eyelets. I would only buy double eyelets since I have had cases where single eyelets have pulled thru.
Here is a table of key comparisons for some 700 C rims, followed by a brief discussion of each column: (See Berto for a much more complete table):
Rim Tire Recommended Model-----------------------Weight--Width-Width -----Use-----------
Mavic Open 4CD 420 19 18-23 triatheletes Mavic MA 40 430 20.5 19-22 triatheletes Mavic Module 3CD 530 22 22-28 touring Mavic Module 4 550 26 28-35 expeditionAraya 700C Japan 25 28-35 Miyata 1000 touring Wobler Super Champion 20 Ambrosio 19 Super Elite 530 20
However, I would still go for the width recommended by the manufacturer for the tire you want, and not try and go much narrower just to save weight. Also a wide rim is easier to insert and take off the bike because the brakes can be set wider.
4. Buying Spokes
Almost all quality wheels built today are made with stainless steel spokes. There are both "butted" spokes and straight guage spokes. Straight guage spokes are easier to build a wheel with because they don't "wind up" when you are turning the nipple. Similarly, thicker spokes are easier.
The most widely available spokes are made by a Swiss company called Drahtwerke Trefilerie (DT). Straight guage spokes come in two standard thicknesses:
1.8 mm (15 guage)
2.0 mm (14 guage)
Nipples: The nipples from 1.8 and 2.0 mm spokes cannot be swapped, they are different diameters. Later in this document it is handy to have some standard terminology for referring to nipples. The "head" of the nipple is the end with the screwdriver slot in it. The other end is called the "tail end" or "spoke end".
When I first started, I assumed there would be some agreed upon specification for every rim and hub, and that all you had to do was quote those specs, and get the right spokes. This is not true.
Most people rely on the shop to sell them the right length of spoke when they buy their rim and hub. The shop determines the proper length by directly measuring certain things on the rim and hub, and then using various charts and tables to get the proper length. Unfortunately these charts are not standardized as to what measurements they start from. In particular, they don't agree on the method of specifying how far the nipple is indented.
Therefore, I standardized on certain measurements anybody can do and wrote a computer program to calculate the corresponding spoke lengths. The name of the program is "spoke.exe". To find out how to run it, stick the floppy into an IBM compatable computer and type "A:spoke". A help message will come up telling you the inputs you require:
spoke RimDiam HubDiam ShortOffset LongOffset RimHoles CrossEg:spoke 592 44.2 18 38 36 3
Here are the answers for several common sets of input:
!--answers-->
!
Rim Hub Short Long ! Short Long Hub and Rim Diam Diam Offset Offset Holes Cross ! Spoke Spoke --------------------------------------------------------------------------- Shimano 105-Ambrosio 592 44.2 18.0 38.0 36 3x ! 294.6 296.5 Shimano 105-Ambrosio 592 44.2 18.0 38.0 36 4x ! 302.0 303.9 Shimano 105-Ambrosio 592 44.2 18.0 38.0 40 4x ! 299.0 300.9
How the program does the calculation is explained in a separate document. For now, all you need to know is how to do each measurement, to get the numbers.
A more convenient way to measure this is to stick two nipples in opposite holes and measure the distance from the tail end of one to the tail end of the opposite. In this case, all you are missing is the part of the spoke that is inside the nipple. This length is about 10.5 mm when the spoke is threaded all the way into the nipple such that the spoke end is flush with the bottom of the nipple slot.
In my program, I just ask you to measure the distance from tail to tail and call this "rim diameter". The thing I call rim diameter is really the diameter of the circle formed by the inside ends of the nipples. I add the 10.5 mm of thread inside the program.
How to measure: Put two standard spoke nipples into opposite holes on the rim and measure the distance between the nipple ends. Since the nipples are sometimes difficult to hold in place with your fingers, you can hold them in place by threading 2 spokes backwards into the nipples, and then push them into place with the spokes. Put the rim on a bench with a ruler underneath it. A typical measurement for a box section rim like Ambrosio is 592 mm.
How To Measure: Use a vernier calliper and move the jaws so that half the hole is covered. A typical value is 44 mm for a Shimano 105 or Shimano 600 hub.
How to Measure: The easiest method I found to calculate the offsets is to trace the flange distances and nut distances directly onto a piece of paper. It is as if you rolled the hub across the paper, and the flanges left marks. To get corresponding marks for the nut ends, look straight down from above and drop a mark from each end. Once you have the marks, measure the distance between the outside of the lock nuts and mark the center. Once you mark the center, you can measure the offsets right off the diagram.
You can check the accuracy of your diagram by making sure that the "over locknut" distance is 126 or 130 or 135 mm, same as your dropouts.
The diagram below shows the following:
Center!
! !
! !---long -----!
!--short-! offset !
! ! offset ! ! !
! ! ! ! !
! _____________! ! ! !
! ! ! ! !
! ! ! ! !
! ! ! ! !
! ! ! ! !
! ! ! ! !
! ! ! ! !
! ! ! ! !
! _____________! ! ! !
! ! ! ! !
! ! ! ! !
! ! ! ! !
left ! right
nut short ! nut
side ! LongSide
flange ! flange
Typical measurements for a Shimano 600 or 105 hub are:
Distance between nuts: 126.5 mm (standard for all road bikes)
Distance between flanges: 56.0 mm
Long Offset 38.0 mm
Short offset 18.0 mm
Column 6 - Cross (3 cross or 4)
Defintion: The cross pattern you want to build when you build the wheel. eg: 3 cross or 4 cross. For radial spoking (which I don't recommend), use 0 cross.
e. Rim Tapes
When buying your rim, don't forget to buy a rim tape. The job of a rim tape is to protect the inflated tube from rubbing against the spoke ends. There are three types: Plastic, Tape, and Rubber (traditional) I prefer the plastic ones, providing they fit correctly.
5. Familarization with Existing Wheels and Components
This section discusses both things you should be familiar with before you start the actual procedure,and also design issues you should resolve in your own mind before building. It helps to look at a few existing wheels, and especially the components you have bought as you read this section.
Three cross wheels are stiffer radially, but may not distribute the load among the spokes as well. Four cross wheels have longer, more tangential spokes. These give a slightly softer ride, and may "wind up" a little less under torque than a three cross pattern. However, 4 cross spokes in a 36 hole rim tend to cross over the spoke ends, making it difficult to remove and replace a broken spoke.
The trend nowdays is to always use 3 cross for 36 hole rims. However, there are still numerous books which recommend 4 cross for heavier riders. When you get to 40 and 48 hole rims, 4 cross make increasing sense. To understand this, consider that as you increase the number of holes but stick with the same number of crosses, the spokes become increasingly radial.
c. Spoke Holes Staggered on Rim
Notice that the holes in the rim are staggered left and right. They are not centered on the rim. When you are building a wheel, the spokes in the left flange must be connected with the left staggered holes. I refer to this as the "on-side" rim hole. This terminology is used when specifying that spoke one should be connected to an "on-side" hole.
Now that you know about staggering, there are two types of rims, ones that are "right staggered" and ones that are left staggered. By "right staggered" I mean that the first hole ahead of the valve hole is on the right. "Ahead" means as if you were sitting on top of the bike looking down. Most rims are right staggered.
Satisfy yourself that there are in fact two possible types of rim by turning a right staggered rim around, and noticing the hole ahead of the valve stem is still on the right. Or draw both types on a piece of paper, label the left and right staggered rims and rotate it any way you want: the left staggered rim stays to the left. Below is a right staggered rim as you look down. x=spoke and 0=the valve hole.
The lacing procedure I recommend is designed to work for either type of rim, without you having to be aware, but if you try to devise your own procedure, you must make sure it will work for both types.
Looking Down on a Right Staggered Rim:
! !
! !
! x !
! !
! !
! !
! x !
! !
! 0 !
! !
! x !
! !
! !
! !
! x !
! !
! !
Spoke Positions
In a standard wheel, there are only 4 unique positions for spokes: a set of "pulling spokes" and a set of "bracing spokes" on each side. The "pulling spokes are the ones that tend to pull the rim around when you pedal the hub.
Note that as you go round the flange, every second spoke goes from outside to inside and thus has its head on the outside. These are called the "inbound" spokes. The other spokes are referred to as the "outbound" spokes. This distinction will be important when talking about lacing procedures. The two sets of outbound spokes should always be the last to be put in, since they can be more easily swung into place once the inbound are already in position.
Different wheels exhibit all variations as to whether the "pulling" spokes are inbound or outbound. Some wheels use inbound spokes for both sets of pulling spokes. Others use outbound spokes for both sets, and others use one of each. The books say it doesn't make a big difference which way you do it. However, it seems marginally better to make both sets of pulling spokes the inbound spokes. (That way the spokes with the highest tension are the most protected from chain damage.)
Hub Holes Are offset not Opposite
Note that the holes on one side of the hub are half a hole ahead of those on the other side. This makes sense, since each spoke will go to one hole farther around the rim. In a 36 hole rim, the rim holes are 10 degrees apart. Each flange hole is 20 degrees from the previous hole on the same side. Therefore the other flange is offset by 10 degrees.
Spokes either side of Valve Hole Are Parallel
All proper wheels have the spokes on either side of the valve hole parallel. This makes it easier to get at the valve. On the opposite side, the spokes cross sharply, which tends to hold the joint together in the rim. This goal affects all lacing procedures and is the cause of most of the mysterious instructions in the books.
ThreadLock
ThreadLock is a glue like substance which makes sure threaded nuts don't vibrate loose. It is available from automotive suppliers. There are two strengths: (1) Blue more fluid and (2) Red most tight
Ideally, you get it onto the threads themselves as you build the wheel. However, it can also be put onto the nipple after the fact. Although theoretically you put it on the spoke threads, you can also put it onto the nipple, such that it won't turn easily on the rim. Threadlock doesn't seem to cause any problems when you subsequently adjust the spokes, but you probably want to put some fresh threadlock on every spoke after a major truing effort.
6. General Procedure
General Procedure
Below is a general procedure that you can use to build any mirror image wheel: 2,3,4 cross, 32,36,40,48 holes, both pulling spokes on inside or both on outside. You can either work directly from this description, or work from one "instance" of this method, which I describe for a 3 cross, 36 hole, with the pulling spokes on the inside.
The most likely thing to go wrong in any wheel is you don't get both spokes on either side of the valve hole parallel. The only spoke that is not purely intuitive is the first spoke in the second set. Where it goes determines the relationship of the left pattern to the right pattern, which is what has to be correct in order for the two parallel spokes to end up on either side of the valve hole.
Spoke 1 and Set 1
Hold the rim vertically as if you were looking down at your back wheel. The first spoke must meet the following rules:
1. is an inside spoke
2. leads away from the valve hole as you pedal
3. goes into one of the two holes adjacent to the valve hole
Note that these rules force you to start on one side of the hub or the other. Which side they force you to start on depends on where you want your pulling spokes, and what type of rim you have.
With a common "right staggered" rim, and pulling spokes on the inside, you will be forced to start on the non-freehub flange, and connect to the hole BEHIND the valve. No matter how hard you try, you won't be able to start on the freehub side and meet the rules. With a left staggered rim (rare) the rules will force you to start on the other side.
If you change which side of the flange (inner or outer) the pulling spokes are on, you will be forced to start on a different side. Furthermore, since you must still start with the inside spokes, they will be "pushing" spokes.
Once you have the first spoke in place, drop the rest in as a set, and swing them up one by one into place.
Spoke Set 2
The rules for this are:
1. on opposite flange
2. Goes into hub 1/2 hub hole further than spoke 1, in the same direction.
3. goes outside to inside
4. Must go into the second hole from the valve, right after spoke 1
5. similar orientation to spoke 1.
The reason we specify this spoke as spoke 2 is a bit tricky. The thing we are really trying to end up with is the two spokes parallel on either side of the valve stem. However, you can't do that directly in a mirror image wheel, for two reasons: 1. Its harder to figure out which hub hole it should go to. Must count around the holes. 2. As a general rule, always leave the two sets of inside to out spokes to the last, because they can easily be swung into place.
To find the correct hub hole, the key is to understand that since the rim hole you are heading for is one rim hole ahead (10 degrees), therefore the correct hub hole is on the opposite flange and 1/2 hole ahead of the point immediately opposite spoke 1's hole.
Set 3
With the wheel on your lap, drop the third set of spokes into their holes on the lower flange. (Inside to outside). You will now have all the spokes hanging down and swinging free. Then swing each of them up into place, lacing it OVER the last spoke it crosses on its side. This requires the spoke to be bowed slightly to clear the rim.
Set 4
Turn the wheel over and drop each spoke of the 4th set into its hole on the bottom flange. Then swing each of them into place as before, being woven around the last spoke on its side. Notice that each spoke in this set needs to be bowed enough to clear two spokes.
7. Specific Procedure for 3 cross 36 hole
3. Specific Procedure for 3 cross 36 hole
This procedure is a specific example of the previous "general procedure" for the following situation:
- 3 cross wheel
- pulling spokes on the inside of the flange
- right staggered rim (normal)
Spoke 1 - Pulling Spokes on long inside
Insert a "LONG SIDE" spoke from outside to inside and connect it with the first hole behind the valve. This will be a pulling spoke. Now twist the hub as if you were pedalling and check that the spoke is pulled back away from the valve hole by the hub. Now insert the remaining 8 spokes in the set.
Spoke 2 - Pulling Spoke on short inside
Insert a SHORT SIDE spoke from outside to inside in the hub hole opposite and just behind the first spoke, and connect it with the second hole behind the valve. Twist the hub as if you were pedalling and check that it is also a pulling spoke in roughly the same orientation as Spoke 1, but 10 degrees behind.
Set 3 - Bracing spokes on outside
Put the wheel on your lap with freehub down and drop 9 SHORT SIDE spokes into their holes in the freehub flange. All 9 spokes will now be hanging freely. Then swing each into place, weaving it under the 3rd spoke it crosses. Check to make sure it goes to the correct side of the rim, and looks the right length.
Set 4 - Bracing spokes on outside
Turn the wheel over on your lap and drop the last 9 spokes into their holes and as before swing them into place. Weave the spoke under the third spoke it crosses as before. Notice that this time you have to clear two other spokes at the rim before you are in the right place.
Inspection
Inspect the two spokes on either side of the valve to make sure they are parallel with one going each way. Now tighten all the spokes till only the last thread is showing. I use a power drill with a countersink bit for this.
8. Truing Algorithm
The dictionary defines "algorithm" as: "a procedure for solving a
mathematical problem in a finite number of steps that frequently involves repetition of an operation". This is exactly what we want for truing a wheel. An approach I used for years was to just keep adjusting various problem areas on an ad-hoc basis, and hoping the wheel eventually became true. This approach is discouraging and inefficient because there is no guarantee there is a finite number of steps. Therefore I developed the algorithm below, which converges on a solution in very few steps, but every step requires analysing exactly which spoke(s) should be adjusted.
The overall method is to start with a loose wheel, and then gradually tighten"problem" spokes until the wheel is true and round. To make sure you are truly systematic, label the spoke holes 1 to 36, and jot down your analysis in each case.
Start by identifying the location of the 2 or 3 worst problem areas. Eg: Between 20 and 28 there is a bad high spot. Once you have surveyed the whole wheel, work on the worst problem first. A roundness problem is more serious than a side to side problem of the same size because it takes much more adjustment to get rid of a roundness problem.
Now the most important part: figure out exactly the right adjustment in a given problem area. There are four steps:
1. Describe problem area: Eg: 10-20 high and pulls to left
2. Define Expected Problem spokes: Eg: Must be loose spokes on the right.
3. Do Complete Tension Analysis: Eg: 16, 18 are loose, the rest are about even tension.
4. Decision: Tighten 16 and 18 by 1/4 turn.
It is important to do a complete tension analysis before adjusting even one or two spokes. Test every spoke's tension and record the results, then review the list again. Be on the lookout not only for the expected problem spokes, but also for unbalanced tensions. Only when you are sure you have the whole picture, make the adjustment. Spoke tensions can be measured by plucking the spoke with a screwdriver at the nipple.
From time to time, check the whole wheel for tension problems. A typical serious problem is one spoke that is very tight which is compensated for by adjacent spokes that are too loose. This is what I call an "unbalanced" situation, and must be equalized before going further.
If you keep applying this method, in 8 oror 10 steps you will converge on a round, straight wheel with relatively even spoke tensions. However, if you make too big an adjustment, you may overshoot the solution, and then start going in circles. If it seems that your whole wheel is getting too tight, or you are going in circles, it seems that the best thing is to loosen every spoke several turns and come at it again. Theoretically you should be able to just loosen "low spots" and work backwards, but sometimes this doesn't work.
The key to this method is to spend more time analysing and thus do less adjustments. Because your analysis deals with both roundness and alignment in a given area at the same time, you cut down the list of possible adjustments.
If you only try to solve one of the two problems at a time, you can easily do adjustments that have to be undone later.
For example, if you concentrate on roundness only you may overtighten one of the sides beyond its final solution. When you later tackle side to side problems, you may try to tighten the other side. The result of this will be that both sides are too tight, and the wheel has a low spot. The result of this kind of methodology will be that you iterate back and forth around the solution rather than smoothly converging by doing exactly the right adjustment first.
9. References
6. References
Upgrading Your Bike - Frank J Berto
I was really excited when I got this book because of its structure. This book is well worth owning, especially for contempory parts
selection. He discusses the general principles, and systematically discusses each attribute of each component, then lays out a comparison table. He does this for all the common components. Eg: All about wheels. He doesn't tell you how to repair a wheel.
Complete Book of Bicycling - Sloan
This book contains a very long confusing mindless description of how to build a wheel, and is exactly the reason why you should go back to first principles and derive your own simpler method. There is little description of "why" in the book.
The Bicycle Wheel - Jobst Brandt
This book is very elegant, and is probably the biggest seller for wheel building. However, although it is filled with impressive technical calculations, most other books are not convinced that a wheel "stands" on its bottom spokes. Its pretty hard to argue with the fact that at any given time, the top spokes have more tension in them than the bottom. I think the point he wanted to make was that the spokes that vary the most under load are the bottom spokes, since the load is spread much more evenly on the top.
Also I found his method of lacing to be somewhat less than intuitive. Also, I found that his analysis lacked much of the real information that you need to build a wheel, such as how to calculate spoke lengths.
Carlton Cycle
It is very worthwhile to talk with both Chris and Cliff Green about different hubs and rims. Chris is familiar with all the main standards of design for hubs, and knows what can be interchanged with what. Carleton supplied me with photocopies of various rim catalogs, from which I was able to make much better rim decisions than I had previously made.
Summary of Useful Tools
- a truing stand
- A vernier calliper to measure the thickness of spokes, width of rims, etc.
- A dishing tool (about $30.00)
- Screwdriver for spoke nipples
- threadlock (blue)
Credits
Since this page gets such a huge number of hits, you
may as well know about two other people that have made
a contribution on the planet: Sev Heiberg and Steve Grant.
(they are both Bivouac Authors as well)
Steve Grant: was one of the top wheel builders in Vancouver. He lived outside my house in Kitsilano in his green step van. He has been a life long bicycle rider.
Sev Heiberg: helped me think through the math. He was often around during the 2 years my brother and I worked in my garage on various desparate programming projects. His keen mathematical mind was a great asset to me in sorting through many problems. Sev is the same age as my father, and was born in 1921 in Norway. He worked with me for a couple of years while we learned C programming together. Too bad we didn't make a cent!
7. Spoke Calculation Program
Spoke Length Calculation Program