Estimate your paper airplane’s range
Enter your values and press Estimate Range. The result appears below the button and is announced to screen readers. All calculations run locally in your browser.
How this calculator works (two-phase model)
The estimator treats a flight as two connected phases: an initial ballistic climb (like a thrown object) followed by a glide (like a small sailplane). This is a useful mental model because it separates what your arm controls (initial speed and direction) from what the fold controls (how efficiently the plane turns height into distance).
In the ballistic phase, the airplane starts with an initial velocity and rises until its vertical speed reaches zero. The calculator uses basic projectile motion to estimate (a) the time to reach the apex and (b) the horizontal distance traveled during that time. This portion is intentionally simple: it does not attempt to model lift during the climb, and it does not subtract energy for drag.
In the glide phase, the airplane is assumed to transition smoothly into a stable glide from the peak height. The glide ratio (G) tells us how many meters forward the plane travels for each meter of altitude it loses. Multiply the peak height by G and you get an estimated glide distance. Add the ballistic distance and the glide distance to get the total range.
Formulas and assumptions
Let v be throw speed (m/s), θ be launch angle (radians), G be glide ratio, and g be gravitational acceleration (9.81 m/s²). The JavaScript converts degrees to radians and splits the throw velocity into components:
- vx = v · cos(θ) (horizontal component)
- vy = v · sin(θ) (vertical component)
Time to apex is t = vy / g. The horizontal distance during the climb is xballistic = vx · t. The peak height is h = vy² / (2g). The glide distance is xglide = G · h. Total estimated range is R = xballistic + xglide.
Assumptions (what is simplified)
- No air drag during the climb: real drag reduces both height and forward speed, especially for light paper and high angles.
- Instant transition to glide at the apex: the model assumes the plane reaches a peak height and then glides down smoothly without a stall.
- Constant glide ratio: in real life, glide ratio changes with speed, trim, and turbulence; here it is treated as a single number.
- Level ground: launch height equals landing height. If you throw from a balcony, your real distance can be longer.
- Stable flight path: the model assumes the plane does not spiral, loop, or tumble. Stability issues can dominate outcomes.
Worked example (with numbers you can verify)
Use the default inputs to see a concrete example: v = 12 m/s, angle = 35°, and G = 8. The calculator first computes the vertical component of the throw and the time to apex. Then it computes the peak height and multiplies by the glide ratio to estimate the glide distance. Finally, it adds the ballistic distance and the glide distance.
If you want to sanity-check the scale: a 12 m/s throw is a brisk hand launch, 35° is a moderate upward angle, and a glide ratio of 8 is plausible for a well-trimmed glider-style paper airplane. The resulting estimate is typically in the tens of meters, which matches what you might see in a gym or a long hallway when conditions are calm.
Tip: If your estimate seems unrealistically high, reduce the glide ratio first. Many dart-style planes behave more like G = 3–4, while broad-wing gliders may reach 7–10 when trimmed well. Also remember that drag during the climb is ignored, which tends to inflate the estimate for steep throws.
How to measure the inputs (practical methods)
1) Measuring throw speed (v)
You do not need a lab to estimate throw speed. Here are three practical approaches, from easiest to most accurate:
- Use a phone radar/ball-speed app: some apps estimate speed from video or audio. Results vary, but it can be good enough for comparing throws.
- Video timing over a known distance: mark a 5 m or 10 m distance on the floor. Film the throw from the side and count frames for the plane to travel between marks. Speed ≈ distance / time.
- High-frame-rate slow motion: if your phone supports 120–240 fps, you can reduce timing error. This is especially helpful for short indoor flights.
When measuring speed, try to capture the first part of the flight right after release. Paper airplanes slow down quickly due to drag, so measuring later in the flight will underestimate the initial throw speed.
2) Estimating glide ratio (G)
Glide ratio is the most design-dependent input, and it is also the most useful for comparing folds. A simple way to estimate it is to measure how far forward the plane travels while dropping a known vertical distance. For example, if the plane travels 8 meters forward while dropping 1 meter, then G ≈ 8.
A repeatable method is to perform a gentle, level release from a known height (for example, a stair landing or a stage) and aim for a smooth glide. Measure the horizontal distance from the release point to the landing point, and measure the vertical drop from release height to the floor. Then compute G ≈ horizontal distance / vertical drop. Repeat several times and average the results.
If you only have flat ground, you can still estimate G by filming a side view and tracking the plane’s position at two moments. Choose two frames where the plane is clearly visible, measure the approximate vertical drop between those frames, and measure the horizontal travel. The ratio of those distances is an estimate of G.
How to interpret the estimate (and what to do with it)
The number you get is best treated as a baseline under calm conditions. Use it to answer questions like:
- Does increasing throw speed help more than improving glide ratio for this design?
- Is my launch angle too steep for the plane’s stability?
- How sensitive is range to small changes in technique (for example, 30° vs 40°)?
- Are two different folds meaningfully different, or are they within measurement noise?
A helpful workflow is to keep two inputs fixed and vary the third. For instance, keep speed and glide ratio fixed and sweep the angle from 15° to 55°. Then do the same in real life with consistent throws. If the real-world optimum angle is much lower than the calculator suggests, that often indicates the plane stalls when thrown steeply.
Example glide ratios by design
The table below provides starting points. These are not universal constants; paper weight, fold precision, and trim can shift the effective glide ratio. Still, the ranges are useful for selecting an initial value when you do not yet have measurements.
| Design Style | Description | Typical Glide Ratio (G) |
|---|---|---|
| Classic Dart | Narrow wings, pointed nose for speed; tends to descend faster and is less forgiving of trim errors. | 3–4 |
| Basic Glider | Moderate wingspan with slight dihedral; usually stable and easy to tune for smooth flight. | 5–6 |
| Canard Glider | Forward stabilizer helps prevent nose-dive and can improve glide smoothness when balanced well. | 7–8 |
| Competition Glider | Large wingspan and careful center-of-gravity placement; optimized folds and trim for efficiency. | 9–12 |
Troubleshooting and tuning tips (to match the model)
If your measured distance is much shorter than the estimate, the cause is usually not your math—it is the flight behavior. The model assumes a stable climb and a stable glide. Use the checklist below to bring real flights closer to that ideal.
Common issues and fixes
- Immediate nose-dive: the center of gravity may be too far back. Add a tiny amount of weight to the nose (a small piece of tape) or reduce elevator-up bends.
- Stall (climbs then drops abruptly): the launch angle may be too steep or the elevators are bent up too much. Try a shallower angle (for example, reduce by 5–10°) and flatten the trailing-edge bends.
- Spiral or banking turn: wings may be asymmetric. Re-crease the wings to match, check that both tips have the same dihedral, and ensure the fuselage is straight.
- Wobble or flutter: paper may be too light or folds too loose. Sharpen creases, use slightly heavier paper, or add a small reinforcing fold along the leading edge.
- Good glide but short overall distance: throw speed may be lower than assumed. Measure v using video timing, or compare multiple throws to see how consistent your release is.
Technique tips that affect distance
Even with the same design, technique can change the effective inputs. A clean release increases the chance that the plane transitions into a glide instead of wasting energy in a wobble. Aim for a smooth, straight throw with minimal wrist roll. If you are testing designs, keep the throw as consistent as possible and change only one variable at a time.
Indoor testing is often more repeatable than outdoor testing. Outdoors, a light headwind can reduce range while a tailwind can increase it. Updrafts can effectively increase glide ratio mid-flight. The calculator assumes calm air, so treat wind as a separate factor.
FAQ
Is this a “real” physics simulation?
It is a simplified estimator. It uses projectile motion for the climb and a constant glide ratio for the descent. It does not simulate drag, lift curves, or changing angle of attack. The benefit of this approach is speed, clarity, and usefulness for comparisons.
Why does glide ratio matter so much?
Glide ratio multiplies the height you gain. A higher G means every meter of altitude turns into more forward travel. In practice, improving glide ratio through better balance and cleaner folds often yields bigger gains than trying to throw harder.
What if I throw from a higher place?
This calculator assumes launch and landing heights are the same. If you throw from a balcony or stage, your real distance can be longer because the plane has extra altitude to trade for distance. You can approximate that by adding the extra height to the peak height conceptually, but the current calculator does not include a separate “launch height” input.
What values should I start with?
If you are unsure, start with v = 10–12 m/s, angle = 30–40°, and G = 5 for a basic glider or G = 3–4 for a dart. Then adjust based on observed behavior. If the plane stalls, reduce the angle. If it dives, increase nose weight slightly or reduce elevator bends.
By combining measured inputs with this estimator, you can build a simple performance log for each design. Over time, you will learn which folds produce higher glide ratios, which angles avoid stalls, and how consistent your throw speed is. That is the practical value of a simple model: it turns casual flights into repeatable experiments.