Hamburg Abitur Vocational Technology - independent engineering foundations cheat sheet
Hamburg Abitur Vocational Technology - independent engineering foundations · Keep the key ideas within reach.
Statics, strength and mechanical transmission
In an ideal planar model: pin has two force components, roller one normal reaction, fixed support two force components and a moment.
I = b·h³/12, W = b·h²/6 for a rectangle
Simply supported beam, central load: M_max = F·L/4
Euler: P_cr = π²EI/L_k², with L_k depending on the end conditions
Planar DOF: G = 3(n−1) − 2j₁ − j₂
For the defined ideal lossless gear pair, speed and torque-magnitude ratios are inverse; losses reduce actual output torque.
Building systems, load paths, heat and moisture
R=d/λ uses thickness in metres; total resistance includes the model’s surfaces and layers.
U=1/R_total is a steady-state element model, not the complete building energy demand.
Permanent, occupancy, wind and snow actions require the stated design framework.
Moisture, airtightness and intended ventilation must be considered together.
Example tie spacing is supplied data, not a code rule.
Measurement, feedback, PLC and automation
Sensitivity = Δoutput/Δinput; resolution = smallest detectable change
Closed-loop error compares reference and measurement; integral action can remove appropriate steady-state error only under suitable stability and operating assumptions.
PLC scan: read inputs → run program → update outputs
4–20 mA live zero: (I − 4)/16 of the span
Repeatability ≠ accuracy, resolution ≠ sensitivity
Robot DOF come from its joints; workspace is the reachable volume
Energy, thermal machines and environmental assessment
1 kWh = 3.6 MJ; 1 tep ≈ 41.86 GJ
Conversion efficiency must use a consistent useful output and input; it differs from a heat pump coefficient of performance, which can exceed one.
Carnot heat-engine efficiency is1−T_cold/T_hot using kelvin and the stated hot/cold reservoirs.
Hydro: P = η·ρ·g·Q·H
Wind power grows with v³; Betz limit C_p = 0.593
Sustainability is assessed per kWh: CO₂, life cycle, energy mix
Aerodynamic forces and elementary stability models
Lift and drag are defined relative to airflow; a force diagram depends on the stated motion.
The lift-coefficient model is conditional on geometry and flow conditions.
Equal-transit-time airfoil explanations are invalid.
Static restoring tendency differs from dynamic damping.
No classroom result establishes an aircraft operating envelope.
Engineering models, drawings, evidence and project decisions
State the system boundary and assumptions before calculation.
Units, sign conventions and uncertainty are part of the answer.
Verification against a specification differs from validation for an intended use.
Drawings need a declared convention and controlled revision.
Classroom models do not authorize physical operation or structural approval.