# Twelve projects using indirect measurement methods

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Updated: 2026-09-11

## 1. Salt solution and electrical conductivity
- Research question: How well does a linear or quadratic function model the conductivity of sodium chloride solutions derived from voltage and current measurements at constant temperature?
- Raw data: Salt mass, solution volume, reference and sample voltage, current and temperature
- Derived quantity: Concentration, resistance and conductivity
- Mathematics: Calibration, model comparison, residual analysis and uncertainty propagation
- Controls and limitations: Keep electrode geometry, temperature, measurement duration, electrode material, voltage and mixing constant. Low DC voltage and short measurement periods reduce electrochemical effects.

## 2. Battery discharge and delivered energy
- Research question: How do modelled discharge curves and numerically estimated delivered energy differ among battery types under the same resistive load?
- Raw data: Voltage U(t), current I(t) and time
- Derived quantity: Power P(t) = U(t)·I(t) and energy E = ∫U(t)I(t)dt
- Mathematics: Regression, trapezoidal rule, residuals and model comparison
- Controls and limitations: Use suitable low-voltage batteries and loads only; do not short-circuit cells. Document the load, sampling interval and stopping rule.

## 3. Solar-cell angle and energy yield
- Research question: To what extent can a cosine model describe power as a function of a solar cell’s angle of incidence?
- Raw data: Angle θ, voltage U(θ) and current I(θ)
- Derived quantity: Power P(θ) = U(θ)·I(θ) and, if appropriate, integrated energy yield
- Mathematics: Trigonometric regression, optimisation and analysis of model deviations
- Controls and limitations: Control the light source, distance, shadows, orientation and measurement time.

## 4. Newton cooling
- Research question: How does container material affect the cooling constant obtained from temperature-time data for a drink?
- Raw data: Temperature T(t), time and ambient temperature
- Derived quantity: Cooling constant k and characteristic time
- Mathematics: Exponential regression, half-life, residuals and parameter comparison
- Controls and limitations: Keep volume, starting temperature, container geometry, sensor position and environment as constant as possible.

## 5. Air-exchange rate from CO₂ decay curves
- Research question: How do air-exchange rates obtained from exponential CO₂ decay models differ among ventilation strategies?
- Raw data: CO₂ concentration C(t), time, temperature and ventilation state
- Derived quantity: Decay constant and relative air-exchange rate
- Mathematics: Exponential model, parameter comparison and sensitivity analysis
- Controls and limitations: Do not deliberately build up CO₂ in poorly ventilated rooms. Document the initial value, outdoor value, room volume and window position.

## 6. GPS spread and error ellipse
- Research question: How does the GPS position-error ellipse change between open ground, tree cover and dense buildings?
- Raw data: Many coordinate pairs at one fixed location
- Derived quantity: Local x/y deviations, covariance and an error ellipse
- Mathematics: Coordinate transformation, covariance matrices, statistics and ellipse geometry
- Controls and limitations: Use the same device, measurement duration and as comparable satellite conditions as possible.

## 7. Resonance tube and speed of sound
- Research question: How accurately can the speed of sound be determined from resonant frequencies in tubes of different lengths?
- Raw data: Resonance frequency f, tube length L and possibly temperature
- Derived quantity: Speed of sound v from the fitted slope
- Mathematics: Regression of f against 1/L, slope interpretation and error analysis
- Controls and limitations: Document microphone position, excitation method, tube diameter and room acoustics.

## 8. Magnetic field and distance
- Research question: Which power model best describes the measured relative magnetic-field strength along the axis of a permanent magnet?
- Raw data: Relative field strength B, distance d and background reading
- Derived quantity: Exponent n and offset B₀ in B(d) = a·d⁻ⁿ + B₀
- Mathematics: Non-linear regression or log-linearisation, residuals and uncertainty analysis
- Controls and limitations: Keep orientation, measurement axis, zero point, background field and distance measurement consistent.

## 9. Water drainage and differential equations
- Research question: To what extent does the Torricelli model describe the water level in a draining container?
- Raw data: Water height h(t), time, outlet geometry and container geometry
- Derived quantity: Flow parameter k and the linearised quantity √h
- Mathematics: Differential equations, linearisation, regression and goodness of fit
- Controls and limitations: Secure the container and outlet; read water height from the same viewing angle.

## 10. Evaporation: mass loss and airflow
- Research question: How does the evaporation rate obtained from mass-time data change with fan voltage?
- Raw data: Mass m(t), time, fan setting or voltage and temperature
- Derived quantity: Evaporation rate −dm/dt and fitted constant
- Mathematics: Linear, exponential or piecewise models and multiple regression
- Controls and limitations: Document container surface area, liquid amount, fan distance and ambient conditions.

## 11. Video analysis of a projectile path
- Research question: How well does a quadratic model describe the horizontal and vertical position data of a thrown ball?
- Raw data: Pixel positions, frame numbers, frame rate and a length reference
- Derived quantity: x(t), y(t), velocity and acceleration
- Mathematics: Quadratic regression, derivatives, parameter comparison and perspective error
- Controls and limitations: Fix the camera, keep the motion plane approximately parallel to the image sensor and place the scale reference in the same plane.

## 12. Image analysis of dye spreading
- Research question: How does the area of a defined colour-threshold region change as dye spreads in still water?
- Raw data: Image sequence, timestamps, scale and colour values
- Derived quantity: Area, equivalent radius and spreading speed
- Mathematics: Scaling, power or square-root models and regression
- Controls and limitations: Keep camera position, lighting, water volume, drop size and colour threshold constant.