Drag Polar Curve Fitting for Aircraft Using the Curve Fitting Toolbox

Project info

• Field of studyAerospace and Aviation
• LevelMaster's thesis (S2)
• Method typeCommunications and Forecasting
• Estimated build time± 5 working days
• Toolsfittype, fit, confint, predint (Curve Fitting Toolbox)
• PriceUS$25 - US$159

Research goal

Fit drag coefficient curves with the Curve Fitting Toolbox and assess model fit against lift coefficient and wing span efficiency factor.

Variables

Example result

• 0.994R-squared
• 0.994Adjusted R-squared
• 0.135RMSE
• 4.954Peak height a1
• 5.725Peak centre b1
• 2.354Peak width c1

A Gaussian curve fits Drag coefficient against Lift coefficient with an R-squared of 0.994 and RMSE of 0.135; the peak has height 4.95, centre 5.73 and width 2.35, and among four candidate models the best adjusted R-squared is 0.997 (gauss2).

Computed from illustrative synthetic data, not from a real study.

About Curve Fitting with the Curve Fitting Toolbox

The Curve Fitting Toolbox fits curve models (exponential, polynomial, or custom equations) to data using nonlinear least squares. It is used to estimate physical parameters such as decay rates or kinetic constants from experimental data.

Steps

1. 1Prepare x and y data as column vectors
2. 2Choose or define a model with fittype
3. 3Set starting points and parameter bounds
4. 4Fit with fit and obtain gof statistics
5. 5Check parameter confidence intervals and residuals
6. 6Plot the curve, data, and prediction interval

Assumptions to check

• The model form follows the theory of the phenomenon
• Starting parameter values are reasonable so the fit converges
• Measurement errors are roughly random with constant variance

Reading and reporting the results

Report the model equation, parameter values with confidence intervals, R2, and RMSE. Give a physical interpretation of the parameters and compare with alternative models.

Example MATLAB code

A short starting script with this project's variable names. The delivered version is adapted to your data and fully commented.

rng(10);
lift_coefficient = linspace(0, 10, 60)';
drag_coefficient = 4*exp(-0.5*lift_coefficient) + 1 + 0.12*randn(size(lift_coefficient));      % decay with offset

ft = fittype('a*exp(-b*x) + c', 'independent', 'x', 'coefficients', {'a', 'b', 'c'});
[f, gof, out] = fit(lift_coefficient, drag_coefficient, ft, 'StartPoint', [3 0.3 0.5], 'Lower', [0 0 -5]);
disp(f);
ci = confint(f, 0.95);
fprintf('R2 = %.4f, adjusted R2 = %.4f, RMSE = %.4f\n', gof.rsquare, gof.adjrsquare, gof.rmse);
fprintf('Parameter 95%% CI:\n'); disp(array2table(ci, 'VariableNames', {'a', 'b', 'c'}));
fprintf('Half-life = %.3f\n', log(2) / f.b);

figure;
plot(f, lift_coefficient, drag_coefficient); hold on;
pi95 = predint(f, lift_coefficient, 0.95, 'observation', 'off');
plot(lift_coefficient, pi95, 'r--');
xlabel('x'); ylabel('y'); legend('Data', 'Fit', '95% prediction interval');

Packages and prices

Choose how much help you need. Each higher package includes everything in the lower ones. Prices exclude 11% VAT.

• Payment: 50% down payment before work starts, balance after the deliverables are handed over
• Tax: Prices exclude 11% VAT
• Data and academic integrity: Results are computed from your own research data; you write and stand behind your manuscript, we help with the analysis and your understanding of it
• Revisions: Up to 2 revisions are included in the price (Package 3: 3 rounds)

Frequently asked questions