RC Flying Today: Digits & Data
ABSTRACT
- How to weigh a servo
- SIM again
I’ve learned that when I discuss more than two subjects in one column, the extra thoughts tend to get lost when the column folds over to the back of the magazine. From now on I’ll try to keep it to one or two subjects per column.
DIGITS & DATA
Electric-powered models don’t perform well when they’re too heavy. Working with a model should make a modeler gain a strong interest in weight control. Some modelers have purchased a Pelouze PE-5 Digital Postal Scale to weigh model parts. The price is about $60; it weighs objects up to five pounds and indicates weight in either grams or ounces at the touch of a button. It shuts itself off after a few minutes to save battery. But is it accurate enough to weigh a servo (10–15 grams)?
A simple test is to get a handful of copper dimes (1965 to present) and weigh them. A dime weighs 2.268 grams; superficial wear has negligible effect on the weight. Add one dime at a time to the scale, write down the indicated weight, then plot the results. If the trend isn’t a straight line, the machine has a linearity problem. If the trend line is straight but offset, the machine has a scaling or zero-offset problem. Don’t be surprised if the readout doesn’t change when you add a coin or jumps a couple of numbers for one coin.
I put my data into a spreadsheet and let it plot the graph and perform a regression. The regression looked at actual weight as a function of indicated weight and showed the trend line starting about 0.5 gram high and counting less than 0.5% error.
- Regression output:
- Constant: 0.49257
- Std. Err. of Y Est.: 0.683122
- R Squared: 0.997935
- No. of Observations: 25
- Degrees of Freedom: 23
- X Coefficient(s): 1.003524
- Std. Error of Coef.: 0.009516
The PE-5’s internal electronics feed the digital display. Some computers round remainders; some chop them off. In either case the least significant digit (the rightmost) can be incorrect. The PE-5 appears to use round-off because actual weights fall both above and below the trend line. The difference between actual and indicated weight varied from about −0.5 to +0.5 gram. Therefore a scale reading of 10 grams could mean anything from about 9.5 to 11.5 grams.
You also can’t get odd numbers on the PE-5’s grams display — it effectively counts by twos on the gram scale. That creates a large error for small weights (100% error at 2 grams) that diminishes to the regression-derived value (≈0.35% of indicated weight plus ≈0.49 gram) at the high end of the range. The two-gram ambiguity exists throughout the measuring range.
The PE-5 also has an automatic “adjust to zero” feature that can behave oddly. For example, I put paper clips on the scale one by one and the display stayed at zero; then I dumped the whole box on at once and it read 50 grams. How you place a weight on the scale can matter.
Conclusion: don’t rely on a cheap postal scale to weigh servos accurately enough to differentiate similar microservos (Airtronics, Futaba, RCD, etc.). You can weigh heavier items with it, but not small differences of a few grams.
Beam-balance method (easy, accurate way to weigh a servo)
A bright new 1992 quarter weighs 5.670 grams. Here’s a simple beam-balance method you can build in about an hour for about a dollar.
- Materials:
- A piece of 3/8-in.-sq. balsa, about a foot long
- A loop of thread
- A quarter (reference weight)
- Glue
- Steps:
- Put a loop of thread around the balsa and hold it. Slide the loop along the stick until the balsa balances level. Secure (zap or tie) the loop in place — that is your support point.
- Glue the quarter to one end of the balsa.
- Measure the distance from the center (thickness) of the quarter to the support loop. For the example below we’ll assume exactly 6.00 inches (your measured value can be different; use it in the formula).
- Use the balance equation: Reference_Weight × Reference_Distance = Unknown_Weight × Distance.
- With a quarter: D = (Reference_Weight × Reference_Distance) / W
- Reference_Weight = 5.67 g (quarter)
- Reference_Distance = 6 in (example)
- Thus constant = 5.67 × 6 = 34.02
- Example table (Weight in grams → Distance from support in inches):
- 6 — 5.67
- 7 — 4.86
- 8 — 4.25
- 9 — 3.78
- 10 — 3.40
- 11 — 3.09
- 12 — 2.84
- 13 — 2.62
- 14 — 2.43
- 15 — 2.27
- 16 — 2.13
- 17 — 2.00
- 18 — 1.89
- 19 — 1.79
- 20 — 1.70
- 21 — 1.62
- 22 — 1.55
- 23 — 1.48
- 24 — 1.42
- 25 — 1.36
- 26 — 1.31
- 27 — 1.26
- 28 — 1.22
- Notes:
- An avoirdupois ounce weighs 28.349523 grams.
- If you use two quarters as the reference (double the reference weight), the range and sensitivity shift accordingly — useful for differentiating small postal-weight steps such as one vs. two stamps.
- If you need to weigh up to several ounces, use multiples of quarters (1, 2, 4, 8, 16 quarters, etc.), a 35mm film container to hold them, and a stronger beam. Your beam balance will be as accurate as the U.S. Mint and the ruler you measure with.
- Typical coin reference ranges (approximate ranges you can cover with each coin as the single reference):
- Penny (1992): 2.500 g — use for 3 to 10 g
- Nickel: covers about 5 to 20 g
- Dime: 2.268 g
- Quarter: covers about 6 to 28 g
- Half dollar: covers about 12 to 45 g
- Dollar coin (recent copper-core type, not Susan B. Anthony): covers about 27 to 100 g
If you prefer, you can compute the scale distances automatically with a small computer program. Below is a BASIC program that checks common U.S. coins and prints scales for grams or ounces.
BASIC program to calculate scales for a beam balance
(To print on a printer, substitute LPRINT for PRINT.)
10 INPUT "1992 PENNY, NICKEL, DIME, QUARTER, HALF, OR 1971-78 CU DOLLAR (P N D H Q X)";A$ 20 IF A$="P" OR A$="p" THEN R=2.5: C$="PENNY": GOTO 80 30 IF A$="N" OR A$="n" THEN R=5: C$="NICKEL": GOTO 80 40 IF A$="D" OR A$="d" THEN R=2.268: C$="DIME": GOTO 80 50 IF A$="H" OR A$="h" THEN R=5.67: C$="QUARTER": GOTO 80 60 IF A$="Q" OR A$="q" THEN R=11.34: C$="HALF DOLLAR": GOTO 80 70 IF A$="X" OR A$="x" THEN R=22.68: C$="DOLLAR COIN" 80 INPUT "GRAMS (G) OR OUNCES (O)";A$ 90 IF A$="G" OR A$="g" THEN B$="GRAMS" 100 IF A$="O" OR A$="o" THEN B$="OZ" 110 PRINT 120 PRINT B$;" INCHES" 130 IF A$="O" OR A$="o" THEN GOTO 230 140 REM COMPUTE GRAMS SCALE 150 FOR W=1 TO 300 STEP 1 160 D=6*R/W 170 IF D>6 THEN 210 180 IF D<.5 THEN 210 190 PRINT USING "##.##";W; 200 PRINT USING " #.##";D; 210 NEXT W 220 GOTO 10 230 REM COMPUTE OUNCES SCALE 240 FOR W=.1 TO 30 STEP .1 250 D=6*R/(W*28.3495237) 260 IF D>6 THEN 300 270 IF D<1.5 THEN 300 280 PRINT USING "##.#";W; 290 PRINT USING " #.##";D; 300 NEXT W 310 GOTO 10
Transcribed from original scans by AI. Minor OCR errors may remain.
