BEML Junior Executive cheat sheet

Lift equation: L = ½ρV²S·C_L; induced drag D_i = L²/(½ρV²πe·b²), so doubling span quarters induced drag at fixed lift.

Thrust-to-weight ratio governs climb and acceleration; wing loading W/S governs stall speed since V_stall = √(2W/(ρS·C_Lmax)).

Swept wings delay drag divergence by raising critical Mach number; drag divergence typically begins near M 0.85 for thin unswept airfoils.

Turbojet vs turbofan: bypass ratio BPR = bypass mass flow / core mass flow; high BPR raises propulsive efficiency at subsonic speeds but reduces specific thrust.

Specific fuel consumption (SFC) is fuel flow per unit thrust (TSFC, kg/(N·h)); lower TSFC means better range.

Breguet range equation: R = (V/SFC)·(L/D)·ln(W_initial/W_final); payload-range trade-offs follow directly from it.

Radar range equation: R_max ∝ (P_t·G²·λ²·σ/(noise))^(1/4); halving target RCS σ reduces detection range by about 16%.

Standard atmosphere at sea level: 101.325 kPa, 15 °C, density 1.225 kg/m³; temperature lapse rate 6.5 °C per km up to 11 km.

Ripper production = (bucket or blade volume × cycles per hour) × job efficiency; cycle time includes dig, swing, dump, and return.

Excavator cycle time rule: productivity falls roughly in proportion to swing angle; a 90° swing is the reference, and 180° swing cuts output by about 20-30%.

Bucket fill factor: heaped capacity = struck capacity × fill factor (typically 0.8-1.05 depending on material and bucket type).

Swell factor: loose volume = bank volume × (1 + swell %); compacted volume = bank volume / (1 - shrinkage %).

Dozer production uses blade capacity, push distance, and a fixed-time component; slot dozing improves blade load by keeping material between tracks.

Load factor and match factor: match factor = (trucks × truck cycle time)/(loaders × loader cycle time); a value near 1.0 balances the fleet.

Haul-road grade resistance ≈ 10 kg per tonne per 1% grade (about 1% of weight); total resistance = rolling + grade + curve resistance.

Crawler undercarriage wear is driven by abrasiveness and sprocket/idler alignment; track tension is set per manufacturer's sag specification, usually measured at mid-span.

Rock drill performance is measured by penetration rate; specific energy (energy per unit volume removed) falls as thrust and rotation speed are optimized for the rock type.

Cant (superelevation) equilibrium: h_eq = G·V²/(127·R) with h in mm, G in mm, V in km/h, R in m; actual cant is limited by passenger comfort and applied with cant deficiency.

Maximum speed on a curve: V_max = √((h + d)·R/11.8) for broad-gauge Indian conditions, where d is permitted cant deficiency in mm.

Transition length L = (h·V)/(maximum rate of change of cant); a typical limit is 35-55 mm/s for the rate of cant gradient.

Rail expansion: ΔL = α·L·ΔT, with α ≈ 1.15 × 10⁻⁵ per °C for steel; continuous welded rail needs a stress-free temperature and adequate ballast resistance.

Track modulus and stiffness govern dynamic wheel load; sleeper spacing, ballast depth, and rail section (kg/m) determine vertical stiffness.

Signalling headway: minimum headway time = (train length + braking distance + overlap + sighting)/speed + dwell time; metro design headways are often 90-120 s.

Traction power: P = F·v; adhesive limit F_max = μ·W, with μ typically 0.15-0.30 depending on wheel-rail contamination.

Third-rail DC traction commonly uses 750 V DC; 25 kV AC overhead is standard for mainline electrification; return current path and stray current control matter for metro tunnels.

Metro tunnel ventilation and fire safety rely on longitudinal or transverse ventilation; emergency egress walkways and cross-passages are spaced per fire-life-safety norms.