Select shape, fluid, velocity, and temperature to compute drag force, Reynolds number, terminal velocity, and power. Plots F_D vs velocity and C_D vs Re curves in real time.
Parameters
Shape
Custom C_D
Reference Area A
m²
Fluid
Temperature T
°C
Affects density and dynamic viscosity
Velocity v
m/s
Weight W (for terminal velocity)
N
Flow Visualization — Flow Past a Body & Wake (Live)
Bluff bodies (sphere, flat plate, cylinder) separate the flow into a large turbulent wake and high drag. A streamlined body keeps the flow attached with a tiny wake — about 1/12 the drag. The drag arrow grows with v².
Results
—
Drag Force F_D [N]
—
Reynolds No. Re
—
Terminal Vel. v_t [m/s]
—
Drag Power P [W]
Drag Force F_D vs Velocity v
C_D vs Reynolds Number Re (sphere, empirical)
CAE Note
Pre-CFD hand-calculation for OpenFOAM / ANSYS Fluent aerodynamic simulations. Same form as LS-DYNA fluid–structure interaction (FSI) drag term. Also used for drop-test terminal velocity checks, vehicle fuel-economy drag estimation, and wind tunnel data verification.
What exactly is the drag coefficient, C_D, that I'm selecting for different shapes in the simulator?
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Basically, it's a dimensionless number that quantifies how "slippery" or "bluff" a shape is in a fluid. A low C_D (like 0.04 for a streamlined airfoil) means it slices through easily, while a high C_D (like 1.3 for a flat plate facing the flow) means it creates a lot of resistance. In the simulator, try switching from a "Sphere" to a "Cube" and watch how the drag force instantly increases for the same velocity.
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Wait, really? So if drag force depends on velocity squared, does that mean going twice as fast creates four times the drag?
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Exactly right! That's the $v^2$ term in action. For instance, a car at 100 km/h experiences four times the aerodynamic drag it does at 50 km/h. You can see this dramatic effect in the simulator's plot. Try slowly moving the "Velocity (v)" slider up and watch the "Drag Force (F_D)" line curve upward sharply.
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That makes sense. So what's terminal velocity? Is that just when the drag force can't get any bigger?
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Not quite. Terminal velocity is the constant speed reached when the upward drag force perfectly balances the downward weight. No net force means no more acceleration. In practice, a skydiver reaches it after a few seconds of freefall. In the simulator, enter a "Weight (W)" and see the "Terminal Velocity" result update. Change the fluid from "Air" to "Water" and see how much slower the terminal velocity becomes because density ($\rho$) increases.
Physical Model & Key Equations
The primary equation calculates the aerodynamic or hydrodynamic drag force opposing motion. It shows force depends on the fluid density, the object's frontal area, the square of its speed, and its shape's drag coefficient.
$$F_D = \frac{1}{2}C_D \rho A v^2$$
$F_D$ : Drag force (N). $C_D$ : Drag coefficient (dimensionless, set by shape). $\rho$ : Fluid density (kg/m³, depends on fluid & temperature). $A$ : Reference area (m², typically frontal area). $v$: Velocity relative to fluid (m/s).
When an object falls under gravity, it accelerates until drag equals weight. Setting $F_D = W$ and solving for velocity gives the terminal velocity. This is a crucial check for drop tests and parachute design.
$$v_t = \sqrt{\frac{2W}{C_D \rho A}}$$
$v_t$ : Terminal velocity (m/s). $W$ : Weight of the object (N, $W=mg$). The equation shows why a parachute (large $A$ and $C_D$) drastically reduces $v_t$ for a safe landing.
Frequently Asked Questions
A shape preset uses a fixed CD value for the drag calculation. The CD-Re chart is a sphere-only reference and does not feed back into the selected-shape drag calculation. Use custom CD when you need a specific value.
Terminal velocity is the speed where drag balances the object weight W [N]. The input is weight, not mass. The marker on the drag-vs-velocity chart shows the current operating point; terminal velocity itself is reported in the result card.
The CD-Re curve shown here is the empirical curve for a sphere only. It is a reference display independent of the fixed CD used for the selected shape in the drag calculation.
Changing the temperature alters the density and viscosity of the fluid (air or water). A change in density directly affects the magnitude of the drag force, while a change in viscosity alters the Reynolds number and thus the drag coefficient. This allows you to simulate differences in air resistance between high and low temperatures.
The Drag Equation and the Drag Coefficient
The drag force (air resistance) $F_D$ on a body moving through a fluid is given by the following equation.
$F_D = \dfrac{1}{2}\,\rho\, v^2\, C_D\, A$
$\rho$ is the fluid density, $v$ the relative velocity, $A$ the frontal projected area, and $C_D$ the drag coefficient (a dimensionless number determined by shape). Because drag is proportional to the square of the velocity, doubling the speed quadruples the drag. This is why air resistance becomes dominant at high speeds.
Drag Coefficients by Shape and the Reynolds Number
$C_D$ depends on shape and the Reynolds number $Re$. Representative values (at high $Re$) are as follows.
Shape
Drag coefficient $C_D$ (guideline)
Streamlined (airfoil)
$\approx 0.04$
Sphere
$\approx 0.47$
Automobile (passenger car)
$\approx 0.25 \sim 0.35$
Cylinder (axis perpendicular to flow)
$\approx 1.2$
Flat plate (perpendicular)
$\approx 1.28$
For a sphere, at $Re\approx2\times10^5$ the boundary layer becomes turbulent and $C_D$ drops sharply (the drag crisis, exploited by the dimples on a golf ball). The terminal velocity is the speed at which gravity and drag balance, given by $v_t=\sqrt{2mg/(\rho C_D A)}$.
Real-World Applications
Vehicle Aerodynamics & Fuel Economy: Automotive engineers use this exact calculation for initial drag estimation. Reducing a car's $C_D$ and frontal area $A$ directly lowers the force the engine must overcome at highway speeds, improving fuel efficiency. A common target is a $C_D$ under 0.30 for modern sedans.
Skydiving & Parachute Design: A skydiver in a spread-eagle position has a $C_D$ ~1.0 and reaches a terminal velocity of about 55 m/s (200 km/h). A deployed parachute increases the effective area $A$ and $C_D$, reducing terminal velocity to a safe ~5 m/s for landing. This simulator can model both phases.
Wind Load Analysis on Structures: Civil engineers calculate drag forces on buildings, bridges, and signs to design for wind storms. For a large billboard (high $A$ and $C_D$), the force can be enormous, determining the strength of the support structure needed. The "Custom C_D" input is vital for non-standard shapes.
CAE Simulation Setup & Verification: Before running complex (and computationally expensive) CFD simulations in ANSYS Fluent or OpenFOAM, engineers perform these hand calculations. They provide a "sanity check" for simulation results. Similarly, in LS-DYNA for fluid-structure interaction (FSI) problems, this drag formula is often the starting point for the fluid force model.
Common Misconceptions and Points to Note
When using this tool, remember that the reference area A is always a user input. Selecting Flat Plate, Car or Cylinder does not make the tool calculate area automatically. The real pitfall is choosing which area convention to use: frontal projected area, wetted area, diameter times length, or another reference depending on the problem.
Next, the misconception that "the drag coefficient CD is determined solely by shape". It's true you select a shape in the tool, but the actual CD also depends heavily on surface roughness and turbulence intensity. For instance, the dimples on a golf ball intentionally increase roughness to trip the boundary layer into turbulence, causing an earlier "drag crisis" to reduce CD. Keep in mind that the tool's "Sphere" assumes a smooth surface, so its behavior differs from a real ball.
Finally, overconfidence that "terminal velocity is uniquely determined". The tool calculates the terminal velocity of an object in a uniform flow, but in actual falling motion, if the object's attitude changes (e.g., a plate wobbles), the CD fluctuates as well. If you drop a 100g sphere in air, the tool might calculate about 40 m/s, but in reality, wind and turbulence often make it slower. The correct approach is to use it as an estimate of the "theoretical maximum value".
Select a shape preset to use its fixed CD: sphere 0.47, cylinder 1.0, flat plate 1.28, car 0.30, or enter a custom CD.
Enter reference area A manually. A passenger car frontal area is typically about 2.0-2.5 m²; trucks are often 6-10 m².
Reynolds number uses a fixed representative length per shape, such as 0.1 m for a sphere and 1.5 m for a car. Fluid, temperature and velocity update FD, Re, terminal velocity and power.
Example
For the car preset with CD=0.30, A=2.2 m², T=25 °C and v=27.8 m/s (100 km/h), the tool gives FD≈302 N, P≈8.4 kW and Re≈2.7×10⁶ using representative length 1.5 m. At v=33.3 m/s (120 km/h), FD≈434 N and P≈14.5 kW.
Practical Notes
The CD-Re chart is a sphere reference curve; it does not automatically correct the selected shape CD.
Weight W is entered in newtons. Convert mass with W=mg before using the terminal-velocity result.
The definition of reference area A strongly affects FD. Use the same area convention as your comparison data.