Real-time calculation of glider polar curve, best glide speed, minimum sink speed, and MacCready optimal speed. Adjust thermal strength and wind to optimize cross-country performance.
Glider Parameters
Glider Presets
Wing Loading W/S
kg/m²
Zero-Lift Drag CD0
Induced Drag Factor k = 1/(πARe)
Thermal Climb Rate w
m/s
0: none / 2: moderate / 5: strong thermal
Wind Speed (tailwind +)
km/h
Thermal Spacing
km
Starting Altitude
m
Results
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Best Glide Ratio L/D
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Best Glide Speed [km/h]
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Min Sink Rate [m/s]
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Min Sink Speed [km/h]
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MC Speed [km/h]
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XC Speed [km/h]
Glider
Polar
Theory & Key Formulas
Sink rate (as a function of speed): $V_s = \dfrac{C_{D0}}{2K}\cdot\dfrac{W/S}{0.5\rho V}+ \dfrac{2K(W/S)}{0.5\rho V}$
Best glide ratio: $(L/D)_{max}= \dfrac{1}{2}\sqrt{\dfrac{\pi AR\, e}{C_{D0}}}$
MacCready optimal speed: tangent from the $w_{thermal}$ point on the polar curve
What exactly is a "polar curve" for a glider? I see it's the main output of this simulator.
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Basically, it's the glider's performance fingerprint. It's a graph showing how fast the glider sinks through the air ($V_s$) at different forward airspeeds ($V$). The lowest point on the curve is your minimum sink rate—great for staying up. The tangent from the origin gives you the best glide speed for maximum distance. Try moving the Wing Loading (W/S) slider above; you'll see the whole curve shift, showing how a heavier glider sinks faster but can also glide faster.
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Wait, really? So the best glide speed isn't fixed? And what's this "MacCready optimal speed" the tool calculates?
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Exactly! The best glide speed for maximum distance in still air is fixed by your polar. But in a race, you want the best cross-country speed, which balances climbing in thermals and gliding fast between them. That's the MacCready theory. In practice, you tell the system the expected Thermal Climb Rate (w). The simulator then calculates a faster "optimal" cruise speed between thermals. Increase the 'w' parameter and watch the green MacCready ring speed up—it shows you should fly faster when the lift is stronger!
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That makes sense! So the "Wind Speed" and "Thermal Spacing" parameters must change the strategy too. How do they fit in?
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Great question. A tailwind (+ Wind Speed) effectively makes the ground you're flying over pass by slower relative to your airspeed. The MacCready calculation adjusts for this, often telling you to fly a bit slower in a tailwind to conserve height. Thermal Spacing defines the average distance between lift sources. A larger spacing means longer glides, which makes efficient speed-to-sink performance even more critical. Play with these sliders together to see how the optimal speed ring and the predicted final altitude change for a simulated task.
Physical Model & Key Equations
The core of the model is the glider's drag polar, which splits total drag into zero-lift drag and induced drag (from lift generation). The resulting sink rate is power required divided by weight.
$(L/D)_{max}$: Maximum Lift-to-Drag ratio (best glide slope). $AR$: Wing Aspect Ratio. $e$: Oswald efficiency factor. This equation shows why gliders have long, skinny wings (high $AR$) and smooth surfaces (low $C_{D0}$, high $e$).
Frequently Asked Questions
The horizontal axis represents airspeed, and the vertical axis represents sink rate. Each point on the curve shows the sink rate at that speed. The highest point indicates the minimum sink speed, and the tangent point from the origin to the curve represents the best glide ratio (maximum glide distance) speed. The MacCready speed is calculated on this curve based on thermal strength.
For thermal strength, input the average updraft rate (m/s). In actual flight, refer to experience or weather forecasts; for example, try around 1–2 m/s for weak thermals and 3–5 m/s for strong ones. Wind speed affects ground speed calculations, so input the average wind direction and speed at cruising altitude.
The MacCready speed is a theoretical value assuming straight-line flight between ideal thermals. In reality, factors such as thermal strength and distribution, wind changes, and coordination with other aircraft must be considered. In the simulator, first understand the theoretical optimal value, then use it as a guide to adjust according to actual conditions.
After changing the values, be sure to click the 'Calculate' or 'Update' button. Also, entering extreme values (e.g., unrealistic wing loading) may cause the calculation to fail. It is recommended to start with standard glider values (wing loading around 300–500 N/m², aspect ratio around 15–30).
Real-World Applications
Competitive Gliding & Flight Computers: Modern glider flight computers run these exact calculations in real-time. Pilots input the next turnpoint and the expected thermal strength, and the computer displays a "speed-to-fly" bug on the airspeed indicator, which is the MacCready optimal speed you see in the simulator. This is the core algorithm for winning races.
Fixed-Wing Drone & HAPS Endurance Design: High-Altitude Pseudo-Satellites (HAPS) and surveillance drones need extreme endurance. Engineers use this same performance theory, modeled in tools like XFOIL and AVL, to find the wing loading and airfoil that minimize sink rate or power consumption. The simulator's parameters ($C_{D0}$, $k$, $W/S$) are direct outputs from such CAE aerodynamic analyses.
Light Sport Aircraft & Electric Aviation: For aircraft with limited engine power or battery capacity, maximizing glide efficiency extends range and safety. Designers use polar analysis to choose a cruise speed that maximizes range (best glide) or endurance (min sink), a trade-off clearly visualized in this tool's polar curve.
Pilot Training & Briefing: Before a flight, pilots can use a simulator like this to brief performance for the day. By setting the expected wing loading (with water ballast), forecast thermal strength, and wind, they can mentally rehearse the optimal speeds to fly in different phases of the cross-country task.
Common Misconceptions and Points of Caution
Model assumptions: The mathematical model used here relies on simplifying assumptions such as linearity, homogeneity, and isotropy. Always verify that your real system satisfies these assumptions before applying results directly to design decisions.
Units and scale: Many calculation errors arise from unit conversion mistakes or order-of-magnitude errors. Pay close attention to the units shown next to each parameter input.
Validating results: Always sanity-check simulator output against physical intuition or hand calculations. If a result seems unexpected, review your input parameters or verify with an independent method.