E-CodeWind tunnel: airflow over a Joukowski wing — a TI-84 Plus CE program
WINDTUNL is a TI-BASIC program for the TI-84 Plus CE. A wing in a virtual wind tunnel on the TI-84 Plus CE, in colour: 2D potential flow past a Joukowski airfoil from its thickness, camber angle, angle of attack, airspeed and chord. Seven steps: the wing with its thickness and camber, the circulation the Kutta condition needs, the pressure field painted in 8 colour bands, 17 streamlines and a line of smoke (the air over the top reaches the tail first), the surface −Cp chart, lift by Kutta-Joukowski and by the pressure integral (zero drag: d'Alembert), and the lift curve beside thin-airfoil theory.
The field has two settings: quick (5×5-pixel cells, the default: about 30 min on a real CE) or full (all 43,725 pixels: about 50 min on a CE, seconds in E-Calc). Needs the TI-84 Plus CE.
What it asks for and what it shows
It asks for 5 values at its prompts, after you pick option 1 from its menu. In the example below it shows RADIUS , CHORD , THICKNESS , TOP , BOTTOM , SUCTION PEAK -CP, AT X/C, CL=2G/(V·CHORD), ZERO LIFT AT A, SLOPE, THIN AIRFOIL, WING , CIRCULATION , CL , STEP 3 PAINTS THE PRESSURE, QUICK: 5×5-PIXEL CELLS,, ABOUT 30 MIN IN ALL, FULL: ALL 43725 PIXELS,, ABOUT 50 MIN IN ALL, THE MODEL (TEXTBOOK), STEP 1 OF 7: THE WING, ROUND NOSE, SHARP TAIL, STEP 2 OF 7: CIRCULATION, G, STEP 3 OF 7: PRESSURE, 53×33, STEP 4 OF 7: STREAMLINES, NOT AT THE SAME TIME!, STEP 5 OF 7: SURFACE CP, STEP 6 OF 7: LIFT, NO DRAG: D'ALEMBERT 1752, STEP 7 OF 7: LIFT CURVE, CL, (2π PER RADIAN), WINDTUNL · SUMMARY, 1749 CELLS SOLVED (QUICK), (THE NOSE), UPPER SURFACE: SUCTION, LOWER SURFACE: PRESSURE, STAGNATION CP.
Example run
One of its oracle test cases. The inputs are typed in order, and the results are the values the case expects on the screen.
| Step | Value |
|---|---|
| You enter | |
| Menu | option 1 |
| Input 1 | .10 |
| Input 2 | 4 |
| Input 3 | 8 |
| Input 4 | 50 |
| Input 5 | 1.5 |
| The screen shows | |
RADIUS | 1.1027 |
CHORD | 4.033 |
THICKNESS | 11.8 |
TOP | 36.4 |
BOTTOM | 52.2 |
SUCTION PEAK -CP= | 3.78 |
AT X/C= | 0.004 |
CL=2G/(V·CHORD)= | 1.4285 |
ZERO LIFT AT A= | -4 |
SLOPE | 0.12 |
THIN AIRFOIL | 0.11 |
WING | 11.8 |
CIRCULATION | 53.6 |
CL | 1.4285 |
| Text | STEP 3 PAINTS THE PRESSURE |
| Text | QUICK: 5×5-PIXEL CELLS, |
| Text | ABOUT 30 MIN IN ALL |
| Text | FULL: ALL 43725 PIXELS, |
| Text | ABOUT 50 MIN IN ALL |
| Text | THE MODEL (TEXTBOOK) |
| Text | STEP 1 OF 7: THE WING |
| Text | ROUND NOSE, SHARP TAIL |
| Text | STEP 2 OF 7: CIRCULATION |
G= | 4π·VR·SIN(A+B) |
| Text | STEP 3 OF 7: PRESSURE |
53×33= | 1749 CELLS, 5×5 PX. |
| Text | STEP 4 OF 7: STREAMLINES |
| Text | NOT AT THE SAME TIME! |
| Text | STEP 5 OF 7: SURFACE CP |
| Text | STEP 6 OF 7: LIFT |
| Text | NO DRAG: D'ALEMBERT 1752 |
| Text | STEP 7 OF 7: LIFT CURVE |
CL= | 8π·R·SIN(A+B)/CHORD |
| Text | (2π PER RADIAN) |
| Text | WINDTUNL · SUMMARY |
| Text | 1749 CELLS SOLVED (QUICK) |
| Text | (THE NOSE) |
| Text | UPPER SURFACE: SUCTION |
| Text | LOWER SURFACE: PRESSURE |
STAGNATION CP= | 1 UNDER |
How it's checked
9 test cases, each checked against an independent method. Replayed key by key on a virtual TI-84 Plus CE, they make 475 checks.
How E-Code checks every program
Run it or put it on your calculator
- Open the library in the TI-84 Plus CE calculator and pick “Wind tunnel: airflow and pressure over a wing, step by step” (WINDTUNL).
- Put it on your own calculator with a computer and a USB cable, or type it in by hand.
Related programs
- Reynolds number / flow regime
- Potential flow past a spinning cylinder
- Moment distribution for a continuous beam, step by step
- RC circuit charging transient
- Cantilever beam deflection
All TI-84 Plus CE engineering programs · All TI-84 Plus CE programs