---
title: "Lift and drag evaluation in external CFD"
subject: "Applied Computational Fluid Dynamics"
chapter: 6
key: "semester_7/applied_computational_fluid_dynamics:airfoil-lift-drag-evaluation-cfd"
source: https://www.bctengineer.com/q/semester_7/applied_computational_fluid_dynamics/airfoil-lift-drag-evaluation-cfd
site: BCT Engineering
---

# Lift and drag evaluation in external CFD

Applied Computational Fluid Dynamics · Chapter 6: CFD Applications

- Asked in: year not given, 4 marks
- Video: [Lift and Drag in an Airfoil/Wind turbine blade cross section | 2D Analysis | Ansys FLUENT| Workbench](https://www.youtube.com/watch?v=SeIKsFu8MRM) — MECH Tech Simulations
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/applied_computational_fluid_dynamics/airfoil-lift-drag-evaluation-cfd
- Whole chapter: https://www.bctengineer.com/md/semester_7/applied_computational_fluid_dynamics/chapter-6

## Question

Explain how lift and drag on an airfoil are evaluated from a CFD solution. A wing section of chord 0.5 m and span 2 m moves through air ($\rho = 1.2$ kg/m³) at 40 m/s. A CFD simulation gives $C_L = 0.9$ and $C_D = 0.012$. Find the lift, drag and lift-to-drag ratio.

## Short answer

Lift and drag are computed by integrating surface pressure and shear stress and resolving along and perpendicular to the free stream. With planform area 1 m², dynamic pressure 960 Pa, C_L=0.9, C_D=0.012: L=864 N, D=11.5 N, L/D=75.

## Answer

#### Evaluating forces from CFD
The aerodynamic force on a body is the integral of the surface pressure and wall shear stress over its surface $S$:
$$
\vec F=\oint_S\left(-p\,\hat n+\vec\tau_w\right)dS
$$
where $\hat n$ is the outward unit normal. The force is resolved relative to the free-stream direction:
- **Drag** $D$: component parallel to the free stream, made up of pressure (form) drag and skin friction drag.
- **Lift** $L$: component perpendicular to the free stream.

Non-dimensional coefficients:
$$
C_L=\frac{L}{\tfrac12\rho U^2S},\qquad C_D=\frac{D}{\tfrac12\rho U^2S}
$$
with $S$ = planform area (chord $\times$ span). In practice, the CFD code sums the force on each wall face and reports $C_L$ and $C_D$ through "force monitors"; the angle of attack is set by the flow direction. Accuracy requires a fine boundary-layer mesh ($y^+\approx1$ for k-$\omega$ SST), correct transition and separation modelling, and a mesh-independence check. A far-field distance of 10 to 20 chords is used.

#### Numerical
Planform area $S=0.5\times2=1.0$ m². Dynamic pressure:
$$
q=\tfrac12\rho U^2=0.5\times1.2\times40^2=960\ \text{Pa}
$$
$$
L=C_LqS=0.9\times960\times1.0=864\ \text{N}
$$
$$
D=C_DqS=0.012\times960\times1.0=11.52\ \text{N}
$$
$$
\frac LD=\frac{C_L}{C_D}=\frac{0.9}{0.012}=75
$$

**Answer:** $L=864$ N, $D=11.5$ N, $L/D=75$.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. How is the aerodynamic force evaluated from a CFD solution?
   A. Integrating pressure and wall shear stress over the surface, then resolving perpendicular (lift) and parallel (drag) to the free stream
   B. Using only the pressure at the leading edge
   C. Using only the residual values
   D. Using wall shear stress only
   Answer: A. F = integral of (-p n + tau_w) dS; drag is the component along the free stream and lift the component perpendicular to it. (Key point: Force from CFD)

2. For chord 0.5 m, span 2 m, 40 m/s, rho = 1.2, what are S and q?
   A. S = 1.0 m^2; q = 960 Pa
   B. S = 2.5 m^2; q = 960 Pa
   C. S = 1.0 m^2; q = 1920 Pa
   D. S = 1.0 m^2; q = 48 Pa
   Answer: A. S = chord x span = 1.0 m^2, and q = 0.5 x 1.2 x 1600 = 960 Pa. (Key point: Dynamic pressure and area)

3. With CL = 0.9 and CD = 0.012, what are L, D and L/D?
   A. L = 864 N; D = 11.5 N; L/D = 75
   B. L = 864 N; D = 11.5 N; L/D = 0.013
   C. L = 432 N; D = 5.8 N; L/D = 75
   D. L = 11.5 N; D = 864 N; L/D = 75
   Answer: A. L = 0.9 x 960 x 1 = 864 N, D = 0.012 x 960 = 11.52 N, and L/D = CL/CD = 75. (Key point: Lift, drag and L/D)

## Related in Applied Computational Fluid Dynamics

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