Introduction: 300-foot Pocket Tape Measure
How many 300-foot tape measures fit in your pocket and cost under $2?
I had a very nice, somewhat huge, open reel-type 300-foot surveyor's tape measure that worked well until one day it wound funny and I spent a couple of fruitless hours trying to un-jam my $100 measuring investment. I also own an electronic (ultrasonic) tape measure... but that needs a big hard surface to bounce off and only works up to about 30 feet. Actually, you can buy conventional tape measures up to about 25 feet that can be stuffed into a largish pocket... but I want something closer to the size of a 6-foot tape measure. This device is honestly a bit awkward, but it can get the job done and is smaller than an Altoids tin .
I'm sure some readers are thinking "why not just measure what you can with a short tape measure, mark where you stopped, shift the tape measure to there and repeat until the destination, adding the measures to get the total distance?" Glad you asked. Two problems. First, out in the real world, it is hard to be accurate about starting the next measure exactly where the previous one stopped. Second, it is difficult to keep a straight line from start to destination, biasing the result toward overestimation. In summary, accuracy would be much poorer for long distances. Making a calibrated "tape extension" line solves these problems.
Step 1: Materials
Conventional tape measures consist of a tape with calibrated markings spaced at the resolution of the device. For example, a tape measure that reads to a precision of 1/8 inch has the complete length of the tape marked in 1/8 inch increments. To keep accuracy close to precision, the tape is made of a non-stretchy material.
Our "tape" measure also needs to be made of a non-stretchy material, but we can use something much cheaper and more compact than metal, cloth, or fiberglass tape if we don't have to make readable marks on it at the resolution. The trick is to combine a resolution-marked short measuring tape with a less-frequently-marked longer tape or cord -- here we'll use fishing line.
The materials you'll need:
1. An actual tape measure that is way too short. The tiny less-than-$1 ones are usually between 1m and 2m length.
2. A spool of fishing line. To make the line show better for photos, I used 30-pound-test for the unit shown -- don't do that! Cheap 4-pound-test is plenty strong, not very stretchy, fits a much longer length, and is even easier to tie. A spool of 150 yards (450 feet) of 8-pound-test can cost as little as $1.
3. An end for the line. A golf tee or a screw is a good choice if you'll be using this to measure things on the ground; a bent paper clip is a better simulation of the end of a regular tape measure.
If the spool of fishing line you got is one of those flat ones that fits in your pocket, you might be able to bypass step 4 and stow your tape measure within that spool. Otherwise, you'll need to make a spool using either cardboard and scissors or wood and a scroll saw -- as step 4 describes.
Step 2: Tie One On
The first step is to tie the loose end of the fishing line to your end reference point.
This involves making a strong loop at the end of the line. The best knot for this is probably a Bimini Twist -- a well-known fishing knot that any number of WWW sites can help you tie. A Surgeon's Loop (shown in the next step) could be used instead if you're not into twisting. Strength of this knot is critical because this is the one knot you will always be stressing when you make a measurement, and any slippage will hurt accuracy of all your measurements.
Step 3: Measure, Loop, and Repeat
Basically, this is all about tying loops at calibrated spacings in your fishing line. All these knots need to be a type that does not slip -- a Surgeon's Loop is easy and seems to work. Tying experts would probably tell you to use an In-Line Dropper , but I'm not an expert. If the whole concept of tying loops scares you, you can skip this step and use the alternate measuring method of step 6.
Pick an interval that makes multiplication easy and is near the length of, but no longer than, your actual tape measure. Most of us are good enough at multiplying by 3 or 5 feet; metric folks have it even easier using 1 or 2 meters. Keep in mind that the line must be reasonably taught when you are measuring where to put the loops; a friend or a clamp on the other end can help with this.
Carefully and accurately measure the interval distance from your end reference point. You want to tie a loop in the line such that the end of your actual tape measure fits in the loop with the zero position on the tape precisely at the interval distance from your end reference.
The rest of the loops are easy to measure out. Simply measure the interval distance from the previous loop and tie the next loop there. In fact, you don't even need the tape measure to do this after tying the second loop. Because you are simply matching the distance between loops, folding the line back on itself trivially gives the correct distance.
Continue to make equally-spaced loops as far along the line as desired. You might want to wrap the front portion of the line around something while you're doing this, because you certainly don't want 300 or more feet of line getting tangled.
Step 4: Russian Dolls
Remember how Russian dolls nest inside each other? Well, that has nothing to do with this. However, you can use the spool for the fishing line as a holder for the too-short tape measure.
Trace the shape of the tape measure onto a piece of wood just slightly thicker than your tape measure and cut out a shape similar to that shown. This is not a high-precision step. A hole for storing the end screw can be drilled later (when we know where it will fall) if desired. The result is that everything will fit in a little less space than an Altoids tin.
Don't like woodworking? Ok. Simply cut a piece of cardboard in a soft "H" shape to serve as the spool. Many tape measures have a belt clip on the back; if yours does, you can use that to clip your cardboard spool to the back of the tape measure.
Once this is done, tie the loose end of your line to one side of the spool and wrap the line around the spool. Keep the line taught while wrapping it around the spool so that the loops don't get caught under earlier layers of the line.
Step 5: Use
You have built a calibrated extension for your tape measure. The way you use it is quite simple:
1. Fix the end of line reference (screw) to the starting point for your measurement.
2. Roll out the fishing line as though it was a long measuring tape, counting each loop passed as you go. Stop when the next loop would go past the destination.
3. Hook the end of your actual tape measure into the last loop and measure the distance from the last loop to the destination.
4. The total distance is the tape measure distance reading + (the interval length X the number of loops passed).
For example, suppose your short tape measure can handle measuring up to 6 feet, so you put loops every 5 feet in the line. To measure something 16 feet 2 and 5/8 inches long, you would first find that the 3rd loop is the last one before the destination. Hooking the tape measure into that loop gives a measure of 1 foot 2 and 5/8 inches. Adding that to 3 X 5 = 15 feet gives the correct total distance.
Theoretically, the accuracy of measurements made this way is somewhat poorer than you would get with a tape measure calibrated using a primary standard. However, fishing line has lower mass and aerodynamic drag than tape, so it is easier to keep the line straight, and real-world measurement accuracy could even be better than using an actual tape measure. Error for a tape measure is always overestimating the distance, whereas minor stretching and loop placement errors mean the method described in this instructable can slightly overestimate or underestimate the distance. The error for the method given here can be well under 1% -- perhaps a few inches on a 300-foot distance.
Step 6: Tying Loops Isn't Your Thing?
Ok, there is a lot of high-accuracy knot-tying in step 3 of this project. You can trade that for some math.
Still attach the end reference on the line, but don't bother with the in-line loops.
To use it, simply run the line between the start and destination as though it were a measuring tape. The line off the spool is now equal to the unknown distance, but it's probably too large for your actual measuring tape to measure.
You need to make that distance smaller in a known way. Take the end of the line and the spool and run line from both sides through your fingers -- at an equal rate -- until you hit the middle. This takes a little practice, but actually is fairly easy to do. Is that distance short enough to measure? If so, measure it and multiply by 2 to get the actual distance.
If that line was still too long, take the middle point you just found in the line and the end reference and run line from those through your fingers -- at an equal rate -- until you hit the middle of that line segment. If it is now short enough to measure, multiply that distance by 4 and you're done.
If not... well, you get the idea. You keep cutting the measuring problem in half until you can solve it directly, and then multiply the result by the appropriate power of 2 (2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, ...). Note that you are only halving the length of the final line segment, so there are never more than 2 pieces of line running through your fingers. Accuracy is only a little worse than that obtained with the loops -- provided you don't slip and multiply correctly.