CAN IT FLY?
The maker says the drone can carry 25 grams. Ours needs 26. Is there a safety margin? What happens if we work the motors harder? We do the math ourselves, make a prediction, and then test it.
Our math, step by step
Kid version on the left, the numbers on the right. Every step can be checked with a calculator.
Add up every part. The drone and battery are 61 g. Everything we add (the floor camera module, guard, body, window, radio, sensor, wings) is 26 g. Takeoff weight: 87 g.
45 g drone + 16 g battery + 26 g added = 87 g
A prop pushes harder when it is bigger and when it spins faster. Doubling the speed makes 4 times the push. Loaded down, these motors spin about 33,000 times a minute (the box says 45,000 with nothing on them).
Push = Ct x air density x (turns per second)² x (prop size)⁴ = 0.09 x 1.2 x 550² x 0.055⁴ = about 30 g per prop 4 props: about 120 g (anywhere from 100 to 135 g, because Ct and the speed are guesses)
Divide the most push by the weight. That is the thrust-to-weight ratio. Under 1, it cannot take off. 1 to 1.3, it lifts but wobbles and cannot catch itself. 1.5 to 2 flies well. Over 2 is zippy.
120 g / 87 g = 1.38
The maker says 25 g extra. Using our numbers, 25 g extra makes 86 g, and 120 / 86 = 1.4. So their rating keeps about 40% extra push in reserve for climbing, turning and fighting bumps. That reserve is the safety factor. Our 26 g uses up 1 g of it.
Can take off at all: 120 g total = 59 g added (ratio 1.0) Still steady: about 100 g total = about 39 g added (ratio 1.2)
To hover, the props throw air down fast enough to hold the drone up. Physics (called momentum theory) says how much power that takes. Tiny motors and props waste most of their power as heat and swirls, so the battery has to give about 3.5 times more.
Air power = 4 x (push per prop)¹·⁵ / √(2 x air density x prop area) = 5.2 W Battery power = 5.2 W / 0.28 + 0.7 W for the computers = 19.3 W Current = 19.3 W / 3.7 V = 5.2 A
A 600 mAh battery holds 600 milliamps for one hour. We only use 80% of it to keep the battery healthy. Heavier means more power, and the power grows faster than the weight: 10% heavier costs about 15% of the flying time.
480 mAh / 5229 mA = 0.092 hours = 5.5 minutes Flying time goes with (1 / weight)¹·⁵
The C rating says how fast a battery can give its energy. Our battery is rated 20C.
5.2 A / 0.6 Ah = 8.7C to hover. 20C allows 12 A. Plenty of room.
Heavier means shorter flights
Our model for different added weights. Our Rev A adds 26 g.
| Added | Takeoff | Push / weight | Motor power | Current | Minutes |
|---|---|---|---|---|---|
| 0 g | 61 g | 1.97 | about 71% | 3.1 A | 9.1 |
| 10 g | 71 g | 1.69 | about 77% | 3.9 A | 7.4 |
| 20 g | 81 g | 1.48 | about 82% | 4.7 A | 6.1 |
| 25 g (rating) | 86 g | 1.40 | about 85% | 5.1 A | 5.6 |
| 30 g | 91 g | 1.32 | about 87% | 5.6 A | 5.2 |
| 35 g | 96 g | 1.25 | about 89% | 6.0 A | 4.8 |
| 40 g | 101 g | 1.19 | about 92% | 6.5 A | 4.4 |
Working the motors harder does buy more lift, but it costs battery fast and leaves less push for steering. Past about 35 g added, the drone is using nearly 90% of its power just to hang in the air, with little left to catch itself when it tips.
Our prediction
If we add more weight, then the Flying Mosquito will fly for less time and its motors will work harder, because it has to push more air down every second to stay up.
- The four props together push about 120 g at full power (between 100 and 135 g).
- With everything on (26 g added, 87 g total) it flies, but a little slow to climb: about 85% power to hover and about 5.5 minutes per battery.
- With nothing added it hovers about 9 minutes. Each 10 g added costs roughly a minute.
- It can still hover with 35 g added, but wobbles. With about 60 g added it cannot take off at all.
The experiment
Two tests. Run in December (Dec 7 to 13) before the body and guard are final, so the answer can still change the design. No MS-2000 test days.
- 1. Strap the drone to a heavy block, props on and guard onThe block (a 500 g can or a brick in a bag) sits on a kitchen scale. The drone is strapped to the block so it cannot lift off.
- 2. Zero the scaleThe scale now reads 0 with the drone and block on it.
- 3. A grown-up runs the motors at 25%, 50%, 75% and 100% for 3 seconds each from the laptopThe props push up, so the scale reads less than zero. That minus number is the push, in grams.
- 4. Do it 3 times and averageWrite every reading in the journal.
- 1. Charge the battery to 4.2 V and let it cool 10 minutesSame start every time.
- 2. Tape on the nickels for this weight and weigh the whole droneWrite the real grams.
- 3. Press GO in hover mode: take off to 30 cm and hold stillThe laptop saves battery voltage and motor power 10 times a second.
- 4. Stop the timer when the red low-battery light comes on; the drone landsThat time is the flying time.
- 5. Swap batteries, change the weight, repeatWeights in a mixed-up order, so a tired battery does not always land on the heavy flights.
| Nickels | Added g | Real total g | Flight 1 min | Flight 2 min | Flight 3 min | Average | Motor % | Predicted min |
|---|---|---|---|---|---|---|---|---|
| 0 | 0 | ____ | ____ | ____ | ____ | ____ | ____ | 9.1 |
| 2 | 10 | ____ | ____ | ____ | ____ | ____ | ____ | 7.4 |
| 4 | 20 | ____ | ____ | ____ | ____ | ____ | ____ | 6.1 |
| 5 | 25 | ____ | ____ | ____ | ____ | ____ | ____ | 5.6 |
| 6 | 30 | ____ | ____ | ____ | ____ | ____ | ____ | 5.2 |
| 7 | 35 | ____ | ____ | ____ | ____ | ____ | ____ | 4.8 |
Graphs for the board: a line graph of minutes vs grams added (our prediction as a line, the real averages as dots), and a bar graph of push at 25, 50, 75 and 100% power.
What the answer decides
For Addie's science fair
This is a real experiment: one thing changed on purpose (weight), the results measured (time and power), everything else kept the same, and each flight done 3 times. It can be a bonus experiment next to the MS-2000, with its own prediction, data table, graph and conclusion in the journal. The MS-2000 stays the main project, and the flyer only comes to the fair if Miss Taggart allows drones.