I got back into slot car racing about nine months ago after a thirty year-plus hiatus from the hobby. In that time I've built a two-lane Scalextric layout on a 20' by 7 ╜' table. The ninety-plus feet of track is mainly at grade (tabletop level) except for a 17' straight, a 90 degree banked curve, a short banked chute and another 90 degree banked curve. These are at a 3? elevation. Then it's back to grade level and the start/finish line. Fig. 1 shows the table under construction with the elevated structures in place.

Since my track is up at my cabin I've had a lot of weekend racers. Some of them even brought their kids and grandkids. With them I've had a great cross-section of competition and lots of fun. One neighbor, an engineer like I used to be, loved the racing but continually pointed out that something just didn't look right with my banked curves. I knew he was right, and since I don't take criticism very well I decided to have a second look.

It didn't take long to realize that changing a two-dimensional shape (flat track) into a three-dimensional shape (banked track) has an effect on the geometry of the object. The fact is that the radius of the curve decreases as you increase the bank angle. It also decreases the length of track you need to construct a curve of a given arc. In my track's case, it was a pair of 90 curves, but the following analysis holds true for virtually ANY banked curve you may need to build, including banked turns on a routed track.

There are many ways to approach this problem mathematically. However, since I passed addition and multiplication but flunked subtraction and division we'll stick to one characteristic multiplication factor as we work through the process I used in building my banked turns. The same process will work for each ?new? track that follows.

So, get out your calculator with trig functions or use the one that is built into your Windows program (i.e. Start/Programs?/Accessories?/Calculator?) and punch in the value of your bank angle. Then hit the ?cosine? button (cos). The result will be your multiplier. For the example here I am using the SCX outer-outer curve on my Scalextric layout. I chose a bank angle of 25 degrees so my multiplier was .9063. In calculating our new curve radius, we have to have a reference point. Probably the best one to use is the outer radius of the track section. Tracker 2000 says that the SCX outer-outer curve's outside radius is 68.2625 cm (26 7/8?). Using our multiplier, we find that the new radius is 68.2625 cm X .9063 = 61.867 cm (~24 5/16?). We also know that our four sections of ?off-the-shelf? outer-outer curve will give us a 90 curve. However, since we have reduced the radius we must also reduce the track length, but by how much? Once again, we use our faithful multiplier and, since everything is linear (proportional), we can take 90 and multiply it by that same .9063 to arrive at the arc angle we will require. 900 X .9063 = 81.570. To be realistic let's round this angle off to 81 degrees. That means that we will have to remove a 90 arc from one of our track sections. To check out the math, I built a prototype structure using 250 wedges spaced out over a 90 arc with the back of the wedges placed on the new outside radius of 24 5/16? as shown in Fig. 2.

With the wedges fastened, I assembled four SCX outer-outer curves and traced their outline on a piece of 3/16? Luan plywood. Luan is a good material for supporting track if you have elevations or overpasses. It is inexpensive and available at any lumberyard or home improvement outlet. It's also flexible enough to ?give? a little and yet strong enough to support the track quite solidly. It's used extensively as sheeting for inexpensive interior doors so it also has the advantage of being quite stable under varying temperature and humidity conditions.

Next, I cut out the Luan ?pattern? and fastened it to the wedges. I started with the right end fastened flush to the first wedge and continued around the arc until the left end was left hanging out past the last of the wedges. Next, I laid the assembled track sections on the Luan pattern. As expected, they aligned perfectly. Fig. 2 shows the ?overhang? that we get from using the standard track sections. The track to the right of the duct tape is what will comprise our ?new? 90 banked corner. As luck (or higher math) would have it, the overhanging portion appears to be about 40% of a track section. The math agrees. 90 divided by 22.50 gives us exactly .400 or 40%.

The wood strips in the slots are an insurance factor. They are 3/32?+ strips inserted at each of the track joints to assure that there is no ?shifting? of the slot width when we apply heat to shape the track sections to their new banked contour. The heat source I used was an electric heat gun. They get pretty hot so I would suggest that a hair dryer would be more appropriate for those of us who are not into the ?Tim Allen? thing. It's surprising how easily the track settles into its new shape when the heat is applied. The masking tape is to hold the track in position. Of course, by the time the layout is complete it will be secured in a more permanent manner.

Next we have to remove a 90 ?wedge? from one of our track sections. Since we want to maintain the connectors on both ends of the revised track section, we'll have to take the excess out of the center of a section instead of just cutting off one end. As shown in Fig. 3, we can do this by turning an arc of 26 7/8? (the original radius of the track) and drawing a line 0A from the origin to the arc. We can then place a track section on our layout inside these two lines and trace the inside radius and the opposite side. This gives us the outline of a track section (shaded here in green) with a reference point that is the origin of the radius (Point ?0?). If we have a very large protractor it will be easy to mark off the 90 section that will be removed.

Lacking the protractor, we can draw the dashed line AB connecting the outside corners of the track section. When we measure line AB, we find that it is about 10.5?. Dividing that by 2, we can locate the center of the line and thereby the center of the track section, at 5.25?. That is what we have identified as Point ?C?.

Now, since we are experts at proportions we can use them again to find our ?cut lines? for the track. Our goal is to remove a 90 wedge from the 22.50 track section. As shown previously, if we divide 9 by 22.5, we get .4 or 40%. That is the amount of line AB that we will have to remove from this track section. Therefore, we multiply .4 times 10.5? and get 4.2?. Using this number, we measure 2.1? in both directions from point ?C? along line AB. We mark these points and draw a radius from the origin ?O? through each of them. That gives us our two ?cut? lines 1-2 and 3-4. All we have to do now is lay a track section over the outline and mark the track where it will be cut.

Cutting the track is relatively easy. I considered using the band saw, the miter saw, the radial arm saw and the table saw. Each of these seemed to be a bit of overkill so I used a sharp utility knife. I say ?sharp? because sharp tools are much safer and do a far better job than dull tools. Anyway, I cut the plastic with the utility knife and the rails with a cut-off wheel on our Dremel tool clone. If you have access to a bench mounted belt sander you can put a near-perfect gluing edge on your remaining track sections. Use a very light touch, though, because those things are quite aggressive. The lower right-hand corner of Fig. 3 shows the ?cut? track with the ?x? on the portion that is to be removed.

Now you just have to fasten the two outside track sections together to get your ?new? track piece. Alignment is critical so we will want to turn the track upside down on a FLAT surface for gluing. That step is probably the most technically challenging one in this whole process. Don't even bother with CA, epoxy, or any of those plastic solvent adhesives. Scalextric track is made out of polypropylene and even DuPont? doesn't know how to fasten it together. On the positive side, however, FW Tech does know. Try Weldwood Contact Cement. It has marginally good adhesion to the plastic and also maintains the flexibility of the joint. As a suggestion, you should plan to position the ?new? seam over the center of one of your support wedges. This will help in reinforcing the ?new? joint when we get to our last step of attaching the track to the layout surface. For electrical continuity, you will want to solder a short ?jumper wire? across the joint for each of the four rail sections.

Now, while we have gone through an example of how this can work, you should recall that we were using a specific bank angle (250) with a specific section of track (SCX outer-outer curve). In fact, the same analysis will work for any track and any bank angle.

For those of you who are hesitant to cut track, you may still be able to make banked curves out of sectional track but your options will be quite limited. For this approach, you can reverse the math process and obtain your ?multiplier? first and then see what kind of a bank angle you will get.

For our example here, we will go back to our SCX outer-outer curves and design a 1800 banked curve. We know that we would normally use eight track sections for the 180 degree curve. We also know that banking the curve will DECREASE the amount of track required. With this in mind, let's see what happens if we try the curve using only seven track sections. (Please don't overdo this one because FW is charging me a commission on each track section they DON'T sell!)

This one is easy. We just take our new number of track sections and divide by the old number of track sections. In this case it would 7 divided by 8 or .875. SHAZAM, that is our multiplier. Now, to find our bank angle, we just go back to our calculator and hit the ?2nd? or ?INV? button and then the ?COS? button. The result will be our bank angle. In this case, it will be 28.9550. Again, to be realistic, let's make that 290. If you decide to go with this version of a 1800 banked curve, your new outside radius, using the SCX outer-outer curves, will be 68.2625 cm X .875 (the cosine of 290) = 59.7 cm (23 ╜?). I haven't tried this combination, but it falls very close to the Carrera 2/30 banked curve's outside radius of 60 cm. I've been assured that this track has no problems with the ?modern? cars.

Finally, you probably have two questions:

First, will my banked track work with ?modern? cars that may not have a lot of clearance, especially at the front?

The answer is PROBABLY! Since I'm newly back in the hobby, my collection of cars is not awesome. It includes the Fly Viper and Panoz LMP-1 cars. It also contains some Scaly F1s, NASCAR '98 thru 2001s, a caddy, and football cars. Throw in a few odd cars like the MRRC Chaparral?you get the idea. Out of these cars the only one that caused me any problems with my ?old? banked corners was the Scalextric '97 Monte Carlo. It did not deslot but it gave a noticeable ?click? on each of the ?old? banked curves. Fig. 4 is a repainted and redecaled '97 Monte Carlo. It has no clearance problems with my new banked curves. One note of caution, however: if you have cars that you have lowered to any significant degree or which are already close to touching the track in either the front or the back, you may wish to take a second look at any form of banking. A simple twist drill bit is an accurate ?feeler gage? to compare track clearance on various cars. Obviously, clearance is not the only factor in a car negotiating a banked corner but it's a good start. And, of course, you can check any car for clearance problems on your bank just by pushing it around the turn by hand and seeing if it scrapes anywhere. Fig. 5 is just a sampling of the cars mentioned above.

Second, will this ?new? track work with my Tracker 2000 program?

The answer to that question is ABSOLUTELY! However, you will have to ?fool? the program a bit. Again, there are several ways to do this but, since Tracker 2000 does not plot all arc angles in a useable manner (i.e. angles such as 150, 22.5 degrees, 30 degrees and 45 degrees degrees will plot fine but angles like 27 degrees will not), our approach to this will be to leave the number in the ?angle? box the same as it was originally. For example the angle of the SCX outer-outer curve is 22.5 degrees. We will not change that. Anyway, one of the many neat features built into Tracker 2000 is the ability to add ?new? track sections to a manufacturer's standard selection. To cover our two new tracks we can go to the ?Define? tab on Tracker 2000 and bring up the SCX/Scalextric track sections. Click on the outer-outer curve and copy down the eleven specifications for this track.

For the 90 banked curve section, we would hit the ?new? button next to the ?up? arrow on the screen. This will give us a ?new? track in the right column. Name it whatever you think is appropriate. Make sure that you click the ?curve? button under the blank screen on the left. Fill in the eleven blanks exactly as they were on the outer-outer curve except for three of them, the outer and inner travel distances and the outside radius (the inside radius should calculate itself when you plug in the new outside radius and the original track width). Multiply each of those by, guess what, .9063. Respectively, the results should be 22.8358 cm, 19.9353 cm and 61.8663 cm (~24 3/8?). Plug them into the appropriate blanks and you have yourself a ?new? track section. Don't forget to save your ?new? track section by going up to the top ?Define? menu and click on ?Save all Definitions?. If you don't you will go through the whole thing all over again when you reboot your program (guess how I learned that ? YEP!). When we design our layout, we will use four sections of our ?new? track instead of four sections of the original outer-outer curve for every 90 banked curve on our layout. The lane lengths and track inventory will come out as accurately as the original program. In this case, we have ?fooled? the program into thinking that we have four identical ?new? track sections instead of three ?original? sections and one ?oddball?.

The 1800 turn is similar. You have to change the same three values for your ?new? track. The new outside radius will be 68.2625 X .875 (the cosine of 290) = 59.73 cm. (23 ╜?) and the outer and inner travel distances will be 22.0472 cm and 19.2468 cm. Again, name the ?new? section and don't forget to save it.

This time, when we design our layout, we will ?fool? the program by using eight sections of our ?new? track. In reality, however, we will only use seven of the standard outer-outer curves during actual construction. Again, the lane lengths will be accurate but we will reduce our outer-outer curve inventory requirement by one (that's where it starts to cost me money).

The last step in the construction of our banked curve is to fasten the track sections to our layout surface. We must fasten the sections because all plastics have what is called ?memory?. This means that, if they are deformed within reasonable parameters, they will have a tendency, over time, to return to their original molded shape. We, therefore, have to compensate for this ?memory effect?.

On the positive side, the polypropylene plastic used in Scalextric track is a member of the ?Thermoplastic? family of plastics (I have very limited experience with Ninco track but I would suggest that it is made of a similar material). This means that it will deform when heat is applied. Scalextric track ?relaxes? quite nicely under the application of reasonable heat. As mentioned above, I say ?reasonable heat? because our intent here is to ?deform? the plastic, not ?blister? it. The former is reversible but the latter is not. Anyway, the track will conform to the luan substrate quite easily and can be held temporarily with the masking tape shown previously. For permanent installation, the ?Tech Tips? section of the FW website contains an article entitled, ?Fastening Plastic Track to the Tabletop?. Either of the two mechanical attachment methods may work well for you. However, since the only portions of my track that will be fastened down are the banked corners, I plan to take a third approach.

Directly over the wooden wedges (or every alternate wedge ? as the need dictates), I will drill holes through opposite sides of the track at the very outside edge where the borders snap in. These holes will be slightly oversized (5/64?) compared to the #17x 3/4? weatherstrip brads that I will use for the actual fastening process. That will allow the brads to grip the track, the luan substrate and the wedges all at the same time. The oversize holes, coupled with the slight ?give? in the track joints, should compensate for any expansion or contraction due to temperature variations. If you have a ?cut? track, you will wish to use a brad on both sides of your ?new? joint.

In summary and for the record, please recall that I used the Carrera 2/30 banked curve outer radius as a benchmark regarding the functionality of our ?new? curves. In addition, I would guess that a 30 degree bank with our SCX outer-outer curves is starting to approach the practical limit of the track in terms of its flexibility. At some point in time, the flexibility of the pickup rails starts to become the limiting factor.

In any case, I HAVE tried to make a 90 degree bank using only three outer-outer track sections. That required a bank angle of 41.50. While the math worked out, I definitely had the feeling that we were beyond that ?practical? limit. If you plan to test the outer limits of this approach, you may wish to set up a ?prototype? before you take a jackhammer to your track. And keep in mind that the most steeply banked track in NASCAR is only banked 36 degrees.

All things considered, I'm sure that we could find a way to set up a NASCAR tri-oval or any other track configuration using the above analysis ? but that's for another day. Please let me know if you have any questions. I'll be glad to answer any questions you may have if you post them on the Fantasy World Tech Board. Good racing!!

Dale T.

Editor's note on banked turns:

Whenever you create banked turns for your layout be sure to include inside and outside borders in the plan. The outside borders will let the car on the outermost lane blast through the turn at high speed, tail-out, without hitting the wall or guard rail or putting a wheel over the track edge and deslotting. The inside borders provide enough space below the inside edge of the track to allow a deslotted car to slide down out of the path of the car in the inside lane. This will help prevent some truly horrific crashes on your banked turns.