Mechanic - Auto, Marine, Aviation

Tools in this group

• Marine Prop Slip - Theoretical speed, slip percent, and planing vs displacement category from RPM, gear, pitch, and GPS speed.
• Engine Displacement and Compression Ratio - Cubic inches / liters and static CR from bore, stroke, chamber, gasket, deck, and dome volumes.
• Dynamic Compression Ratio - The effective compression ratio measured from where the intake valve actually CLOSES (not from BDC), so it reflects what the cam does to cylinder pressure: from the clearance volume (set by the static CR) and the piston position at intake-valve-closing (slider-crank geometry off rod length and stroke), DCR = (swept-from-IVC + clearance) / clearance. A 4.030 bore, 3.75 stroke, 6.0 rod, 10.5 static engine with a 60-degree ABDC intake close runs about an 8.7 dynamic CR. A big cam closes the intake later, bleeds off charge, and drops the DCR -- which is why a high-static-CR engine with a large cam can still run on pump gas while a mild cam on the same short block detonates. Roughly 7.5 to 8.5 DCR suits 91-93 octane at sea level; altitude and head material shift it. An estimate off the geometry; the cam's actual seat timing, the octane, and the tune govern.
• Bolt Stretch and Clamp Load - Clamp load from F = (stretch * area * E) / grip; cross-check torque.
• Driveshaft Critical Speed - Euler-Bernoulli first-mode critical RPM with safety-factor recommendation.
• Driveline U-Joint Operating Angle and Cancellation - How a Cardan (Hooke) U-joint's operating angle drives a speed fluctuation, and the rule that cancels it. A single joint at angle b swings the output speed between cos(b) and 1/cos(b) of input TWICE per rev -- a peak-to-peak variation of 1/cos(b) - cos(b): 3.1% at 10 deg, 0.3% at 3 deg, 6.9% at 15 deg. A two-joint driveshaft CANCELS it only when BOTH working angles are equal AND the yokes are phased in-plane. So keep each angle small (rule of thumb under ~3 deg at highway rpm) and equal (within ~1 deg). Gives the per-joint variation and the equal-angle check; the exact max angle for a given rpm comes from the U-joint / driveshaft manufacturer's chart (Spicer/Dana, GMB), and the service manual and the measured pinion / transmission / shaft inclinations govern the setup.
• Fuel Energy and Range - BTU and kWh from tank and LHV; range from tank * mpg * load factor.
• Tire Size and Effective Gear Ratio - rev/mi for old vs new tires, effective ratio, cruise speed, recommended axle ratio.
• Tire Contact Patch from Load and Pressure - The tire footprint, and the flotation lever behind airing down: A = W / p, the corner load divided by the inflation pressure. Because the patch carries the load at the inflation pressure, the average GROUND pressure roughly equals the tire pressure independent of load -- which is why airing down floats over sand and cuts soil compaction. A 900 lb corner at 35 psi rides on about 25.7 in^2; drop to 15 psi and the patch grows to 60 in^2 (2.3x) at the same load. An idealization -- the sidewall and tread carry a little load, so the real patch runs a bit smaller than W/p, more so at high pressure. A field estimate, not a measured footprint; the tire, load, and surface govern.
• Brake Pad Lifespan and Heat Capacity - KE per stop, rotor temp rise, wear per stop, estimated pad life by material.
• Valve Flow Coefficient (Cv) - Solve the liquid sizing relation Q = Cv x sqrt(dP / SG) for Cv, flow, or pressure drop; the gas / compressible regime is flagged. Per ISA-75.01 / Crane TP-410.
• Screw / Auger Conveyor Capacity - Volumetric capacity (ft^3/hr) from diameter, shaft, pitch, RPM, and trough loading, and mass rate from a bulk density. Per the CEMA Screw Conveyor standard (Book No. 350); loading fractions user-supplied per CEMA class.
• Horsepower from Torque and RPM - Horsepower, kilowatts, and a solve-for selector across HP, torque, and RPM via HP = Torque * RPM / 5252.
• Volumetric Efficiency and Airflow - Theoretical and actual induction CFM and volumetric efficiency from displacement, RPM, and cycle, with VE above 100% allowed for forced induction.
• Gear-Ratio MPH from RPM - Road speed (or RPM), wheel RPM, and tire revolutions per mile from engine RPM, transmission and axle ratios, and tire diameter.
• Machining Speed and Feed - Spindle speed (RPM) from surface speed (SFM) and cutter or work diameter, plus feed rate (IPM) from the number of flutes and chip load per tooth (first-principles cutting geometry; Machinery's Handbook speeds-and-feeds method).
• Taylor Tool-Life vs Cutting Speed - The Taylor tool-life relation V x T^n = C, the trade-off between cutting speed and edge life: at speed V (sfm) the tool life is T = (C/V)^(1/n) minutes, and the speed for a target life is V = C / T^n. C is the speed for a 1-minute life and n is the tool-material exponent (~0.1-0.15 HSS, 0.2-0.4 carbide), both from the insert maker or a handbook. Because n is small, life is very sensitive to speed: with C = 300, n = 0.2, cutting at 200 sfm gives 7.6 min, but 174 sfm stretches it to 15 min -- a 13% speed cut roughly doubles the life, the number to balance cycle time against insert cost. The base form ignores feed and depth (the extended Taylor equation adds them); the insert manufacturer's data and the tool/work/coolant combination govern.
• Cutter Diameter for a Spindle RPM - The inverse of the machining-speed tile: the cutter or work diameter that runs at a target (or the machine's maximum) spindle RPM for a given surface speed, diameter = 12 x SFM / (pi x RPM). 100 SFM at 1,000 RPM is a 0.382 in diameter. Because a larger diameter turns slower, a machine RPM ceiling sets the SMALLEST cutter that still reaches the full SFM - a smaller one tops out the spindle first. Surface speed from the tool / material chart; the machine and rigidity govern.
• Drill Point Depth - Drill-tip allowance (point length) = (diameter / 2) / tan(point angle / 2) and the tip depth to reach a desired full-diameter depth, for 118 / 135 degree and custom drill points (first-principles drill-point geometry).
• Drill Point Angle from Tip Length - The inverse of the drill-point-depth tile: the included point angle from the diameter and a measured or target point length (tip allowance), angle = 2 x atan( (diameter / 2) / point length ). A 0.5 in drill ground to a 0.15 in tip is a 118-degree point; a shorter tip is a blunter angle. The number you back out when you sharpen to a length or measure a tip on a comparator. Geometry only; the actual grind and web thinning govern.
• Cut Time per Pass - Cut time per pass and total time from cut length and feed rate: feed_IPM = RPM x IPR (or entered directly), t = length / feed_IPM, total = t x passes (first-principles distance over feed rate).
• Material Removal Rate - Material removal rate (MRR) in cubic inches per minute for milling (WOC x DOC x feed_IPM), turning (12 x SFM x DOC x feed_IPR), or drilling ((pi x D^2 / 4) x feed_IPM) (first-principles swept-volume geometry).
• Theoretical Surface Finish - Theoretical turned surface finish from feed and tool nose radius: peak-to-valley Rt = f^2 / (8 x r) with an estimated Ra ~= Rt / 4, in microinches and micrometres (first-principles scallop geometry).
• Feed for a Target Turned Finish - The inverse of the turning-surface-finish tile: the fastest feed per revolution that still holds a target surface finish, f = sqrt(8 x nose_radius x Rt) (a target given as Ra converts with Rt = 4 x Ra). Holding 25 microinch Ra with a 1/32 in nose radius allows 0.005 IPR; a finer 16 microinch Ra drops it to 0.004 IPR. A larger nose radius lets you feed faster for the same finish. Answers 'how fast can I feed' instead of the finish at one feed. Theoretical; leave margin for tool wear and deflection.
• Taper per Foot and Angle - Taper per foot, taper per inch, and the included and per-side angles of a taper from the large and small diameters and the length: TPF = 12 x (D - d) / L, angle/side = atan((D - d) / 2L) (first-principles trigonometry).
• Taper Missing Diameter (Lathe Setup) - The inverse of the taper tile, for cutting a taper to a spec: given the taper per foot, one known end diameter, and the length, the missing end diameter is known -/+ (TPF/12) x L. A 1.000 in large end at 0.600 in/ft over 3 in makes a 0.850 in small end (drops 0.050 in per inch of length); the compound angle per side = atan(TPF/24) = 1.432 deg, which depends only on the TPF so the same setting cuts the taper at any length. First-principles trigonometry; the tool nose radius and setup govern the finished part.
• Tailstock Setover for Taper Turning - The lathe tailstock offset to turn a taper between centers: S = OAL x (D - d) / (2 L). The step people miss: the setover scales with the OVERALL length between centers, not the taper length, because the whole part pivots about the headstock center. A 12 in part with a 1.500-to-1.000 in taper over 8 in needs 0.375 in of setover; if the taper ran the full length it would be just (D - d)/2 = 0.250 in. Offset the tailstock away from the tool to put the small end at the tailstock. Shallow tapers only -- the method swings the center holes off axis, so steep tapers want a taper attachment or the compound. A setup aid; check the first part.
• Dividing-Head Simple Indexing - Simple (plain) indexing on a 40:1 (or custom) dividing head: crank turns per division = ratio / N, plus the exact full-turns-plus-holes setting for each supplied index-plate hole circle that divides evenly (first-principles ratio arithmetic).
• Roller Chain Length in Pitches (ANSI B29.1) - The even-link round-up and corrected center distance people skip: L = 2(C/p) + (N1+N2)/2 + ((N2-N1)/(2 pi))^2/(C/p) pitches. The count must come out EVEN -- an odd count forces a weaker offset (half) link -- so it is rounded UP, and then the center distance is recomputed so the chain fits with proper sag. A 17-to-51-tooth #40 drive (0.5 in pitch) at a 30 in center is 154.49 pitches -> 156 to order, with a corrected 30.38 in center (0.38 in of take-up the skipped step misses); pull the center to 20 in and it is 114.73 -> 116 pitches, 20.32 in corrected. Keep the center at least ~30 pitches for wrap. A design aid; the sprocket selection and take-up govern.
• Sprocket Pitch Diameter (ANSI B29.1) - The pitch diameter a sprocket blank is laid out from, straight from the chain pitch and tooth count: PD = p / sin(180 deg / N). It is the circle through the chain-pin centers when the chain wraps, and it -- not the tip diameter -- sets the drive's speed ratio and center distance. A 17-tooth #40 sprocket (0.5 in pitch) is 2.7211 in pitch diameter, with a maximum outside (tip) diameter OD = p(0.6 + cot(180 deg / N)) = 2.9748 in to turn the blank. A design aid; the manufacturer's tooth form and hub govern the sprocket you cut.
• Tap Drill Size - Tap drill diameter for a target percent of full thread on a 60-degree (UN / ISO metric) thread: % = 76.98 x (D_major - D_drill) x TPI, so D_drill = D_major - % / (76.98 x TPI), with the nearest 1/64 in fraction (the named letter / number drill is a chart lookup) (first-principles thread geometry).
• Spur Gear Tooth Geometry (Diametral Pitch) - From the diametral pitch Pd: pitch dia = N/Pd, OD = (N+2)/Pd, addendum 1/Pd, dedendum 1.25/Pd, whole depth 2.25/Pd, root (N-2.5)/Pd, center distance (N1+N2)/(2Pd). Pd 10, N 40, mate 20 -> PD 4.000, OD 4.200, center 3.000 in; a finer Pd 20 halves every dimension. A shop aid; the gear drawing and AGMA govern.
• Gear Identification (Pitch from Teeth and OD) - Identify an unknown spur gear from a counted tooth count and a measured outside diameter - the inverse of the gear-geometry tile, which needs the pitch you are trying to find. Because OD = (N+2)/Pd, the diametral pitch is Pd = (N+2)/OD, the pitch diameter is N/Pd, and the module is 25.4/Pd. Count 40 teeth on a 4.200 in gear -> Pd 10 teeth/in, PD 4.000 in, module 2.54 mm; the measured Pd snaps to the nearest standard so a caliper a hair off still identifies it. 20-degree full-depth involute; confirm against the drawing or a gear gauge.
• Gear-Tooth Chordal Thickness (Caliper) - The gear-tooth caliper settings the geometry tile leaves out: chordal tooth thickness tc = (N/Pd) sin(90/N deg) read across the tooth, and chordal addendum ac = 1/Pd + (N/2Pd)(1 - cos(90/N deg)) set as the tongue depth. Pd 10, N 40 -> tc 0.1570 in, ac 0.1015 in (the arc thickness pi/2Pd is 0.15708). Standard 20-degree full-depth involute, no profile shift or backlash allowance. A shop inspection aid; the gear drawing and AGMA govern.
• Rolling-Bearing L10 Rating Life (ISO 281) - The cube law that punishes a bearing overload: L10 = (C/P)^p x 10^6 rev, L10h = L10 / (60 x rpm), with p = 3 for ball and 10/3 for roller bearings. A ball bearing (C = 5,000 lbf, P = 1,000 lbf, 1,750 rpm) lasts 125 million rev = 1,190 hr; a 25% overload to P = 1,250 lbf drops it to 64 million rev = 610 hr -- the cube law turns a 25% load increase into a 49% life loss, which is why a small alignment or belt-tension improvement pays off. Basic L10 assumes clean, well-lubricated operation (contamination needs the modified aISO life) and is the life at which 10% have failed, not the average. A planning estimate; the mounting, lubrication, and application govern.
• Max Bearing Load for a Target L10 Life - The inverse of the bearing-l10-life tile: the largest equivalent dynamic load a bearing can carry and still reach a target rating life, P_max = C x (10^6 / L10_rev)^(1/p) with L10_rev = target_hr x 60 x rpm (p = 3 ball, 10/3 roller). A ball bearing rated C = 5,000 lbf at 1,750 rpm can carry 1,000 lbf for a 1,190 hr L10; because life scales as the cube of the load ratio, doubling the required hours only cuts the allowable load by about 20%. Answers 'how hard can I load this bearing' instead of checking one load. A planning estimate; the mounting, lubrication, and application govern.
• Countersink Diameter and Cutting Depth - Dialing a Z-depth when the print calls a diameter: the print gives the finished countersink diameter, but the machine is set to a plunge depth, Z = (D_cs - d_hole) / (2 tan(angle/2)). A 0.500 in countersink, 82 deg inch head, 0.250 in pilot hole needs 0.1438 in of plunge; the same diameter with a 60 deg tool needs 0.2165 in -- a shallower angle drives the tool half again as deep, so the angle callout matters as much as the diameter. 82 deg (inch flat-head) and 90 deg (metric) are NOT interchangeable -- mismatched screw and sink never seat flush, and a few thousandths of over-plunge sits a flat-head proud or buried. A setup aid; the tool geometry and the fastener callout govern.
• Countersink Diameter from a Plunge Depth - The inverse of the countersink tile: the finished (major) diameter a set plunge depth opens, D_cs = 2 Z tan(angle/2) + d_hole, so a machinist reading a dial or a Z stop can check the diameter. A 0.1438 in plunge with an 82 deg tool and a 0.250 in pilot hole opens a 0.500 in countersink; a shallower (larger) angle opens wider for the same depth. 82 deg (inch) and 90 deg (metric) are NOT interchangeable. A setup aid; the tool geometry and the fastener callout govern.
• Shaft Key and Keyseat Size (ANSI B17.1) - The band-table width and H/2 depth machinists mis-read: ANSI B17.1 sets the standard key width from the shaft-diameter BAND, not exactly D/4 -- a 1 in shaft (over 7/8 to 1-1/4) takes a 1/4 in square key, cut to a 0.125 in (H/2) shaft keyseat depth (over-cutting off the full key height weakens the shaft). Key stresses: shear = 2T/(D W L), bearing = 4T/(D H L). At 1,000 in-lb over a 1.5 in key the shear is 5,333 psi and bearing 10,667 psi (both well under a steel key); but a key longer than the hub adds no capacity -- a 1.0 in hub sets the working length, raising shear to 8,000 psi. Square-key model; the allowables and fit class govern.
• Knurling Blank Diameter for Clean Tracking - The blank diameter to turn before knurling so a circular-pitch (TPI) knurl tracks cleanly instead of double-tracking: the blank circumference must be a whole number of teeth, so teeth = round(pi x D x TPI) and blank = teeth / (pi x TPI). A 0.750 in target at 21 TPI wants 49 teeth, so turn the blank to 0.7427 in (0.0073 in under); a 1.000 in target at 33 TPI rounds to 104 teeth and 1.0032 in (0.0032 in over) -- the adjustment is signed and always within half a tooth. Diamond and straight TPI knurls; diametral-pitch knurls and the knurl maker's tracking chart govern the finished pattern.
• Grinding Wheel Surface Speed and Max Safe RPM - The maximum RPM a grinding wheel diameter may turn at its rated surface speed, and whether a grinder's fixed speed stays under it: SFPM = pi x wheel diameter (in) x RPM / 12, so max RPM = rated SFPM x 12 / (pi x diameter). A 7 in wheel rated 6,500 SFPM tops out at 3,547 RPM, so a 3,450 RPM bench grinder runs it at 6,322 SFPM -- within rating; a 10 in wheel rated 9,000 SFPM on a 3,600 RPM machine hits 9,425 SFPM, OVER its rating. As the wheel wears its safe RPM rises but the machine speed is fixed. Per ANSI B7.1; the wheel blotter rating and the machine nameplate are the authority -- never mount a wheel on a faster machine.
• Reaming Prebore (Drill) Allowance - The prebore drill diameter that leaves the right stock for a machine reamer to clean up: drill = reamer diameter - allowance, with Machinery's Handbook stock allowances on the diameter of about 0.010 in under 1/4 in, 0.015 in from 1/4 to 1/2, 0.020 in from 1/2 to 1, 0.025 in from 1 to 1-1/2, and 0.030 in from 1-1/2 to 2. A 1/2 in reamer wants a 0.485 in prebore (31/64 drill); a 3/4 in reamer a 0.730 in prebore. Too little stock burnishes and dulls the reamer, too much leaves an oversize, torn, or bell-mouthed hole. Hand reamers and thin-wall parts take less; the reamer maker's guidance and the material govern.
• Radial Chip Thinning Feed Compensation - The feed correction the speeds-and-feeds tile never makes: at a radial width of cut below half the cutter diameter, the chip is thinner than the programmed feed per tooth, so RCTF = 1/(2 sqrt((ae/D) - (ae/D)^2)) raises the feed to restore the intended chip load. At 10% radial engagement RCTF 1.667 (feed two-thirds higher); at half immersion RCTF 1.0, the crossover where compensation stops. The basis of high-feed and trochoidal milling, and the difference between a light pass that rubs and one that cuts. Radial thinning only. A shop aid; the tool maker's chip load governs.
• Boring Bar / Tool Overhang Deflection and L/D Limit - Why a long boring bar blows the bore and chatters: the tool is a cantilever, delta = F L^3/(3 E I) with I = pi d^4/64, and the L/d ratio sets the chatter risk (steel stable to ~4:1, carbide 6-8:1). A 0.75 in steel bar 6 in out under 100 lb deflects 15 mil (L/d 8, chatter territory); choke up to 3 in and it drops to 1.9 mil (the L^3 law) - the overhang, not the force, dominates, why 'shorten the tool' is the first fix. Static solid-round model, not a stability-lobe analysis. A shop aid; the tool and setup govern.
• Boring Bar Max Overhang for a Deflection Limit - The inverse of the boring-bar-deflection tile: the longest a bar can stick out before its tip deflection reaches the allowable, L_max = (3 E I x deflection / F)^(1/3) with I = pi d^4/64. A 0.75 in steel bar under 100 lb held to 15 mil can reach 6.0 in (L/d 8); a stiffer carbide bar (90e6) reaches 8.6 in. It also flags the L/d against the chatter limit - if the deflection-limited overhang is past ~4:1 steel / 6-8:1 carbide, chatter governs and the real max is shorter. Answers 'how far can I stick out' instead of the deflection at one length. Static solid-round model. The tool and setup govern.
• Ballnose Milling Scallop Height from Stepover - The 3D-finish trade every mold toolpath makes, which turning-surface-finish never covers: a ballnose of radius R stepping over by s leaves a scallop h = R - sqrt(R^2 - (s/2)^2), or the inverse for the stepover that holds a target scallop. A 0.5 in ballnose at 0.030 in stepover leaves 0.45 mil; double the stepover and the scallop quadruples (the s^2 law) - a tighter stepover buys a finer finish at the cost of cycle time. Theoretical flat-surface cusp, not Ra. A shop aid; the real finish depends on the tool, deflection, and slope.
• Fuel Injector Size from Horsepower, BSFC, and Duty Cycle - The first spec of any engine build or boost upgrade, which the displacement and horsepower tiles never give: each injector must flow lb/h = HP x BSFC / (n_cyl x duty). A 400 hp V8 at BSFC 0.50 and 80% duty needs 31.3 lb/h (328 cc/min) per injector; add boost (BSFC 0.60) and it jumps to 37.5 lb/h - a 20% bigger injector for the same power, why a boosted build steps up injector size before adding power. Port injection, entered BSFC; not rail pressure or DI. A tuning aid; the measured fueling and the tuner govern.
• Injector Max Horsepower Capacity - The inverse of the injector-sizing tile: the maximum power an injector set supports - HP_max = injector lb/h x n_cyl x duty / BSFC. Eight 31.25 lb/h injectors at 80% duty and BSFC 0.50 support 400 hp; the SAME injectors on boost (BSFC 0.60) fall to 333 hp, why a richer tune caps power. Enter flow in lb/h or cc/min (lb/h x 10.5 = cc/min). 80% max duty avoids a lean fuel cut. Port injection, entered BSFC; not rail pressure or DI. A tuning aid; the measured fueling and the tuner govern.
• Mean Piston Speed and RPM-Limit Reading - Whether an rpm target is safe for the stroke, the single best predictor of reciprocating stress: MPS = stroke_in x RPM / 6 (ft/min), independent of bore. A 3.48 in stroke at 6,000 rpm runs 3,480 ft/min (street/endurance); rev to 7,000 and it hits 4,060 (performance) - and a longer 4.00 in stroke would already sit at 4,000 at 6,000 rpm, the trade a stroker accepts. Street builds stay under ~4,000, performance 4,000-4,500, race over 4,500. Average, not peak; guidance bands. A shop aid; the component ratings govern.
• Max RPM from a Piston-Speed Limit - The inverse of the mean-piston-speed tile: the maximum safe engine speed for a chosen mean-piston-speed ceiling. From MPS = stroke x RPM / 6, the RPM cap is 6 x MPS_limit / stroke. A 3.48 in stroke at a 4,000 ft/min street ceiling redlines at 6,897 rpm; a longer stroke lowers the cap for the same limit. Street/endurance ~4,000, performance 4,000-4,500, race over 4,500 ft/min. Average, not peak; guidance bands. A shop aid; the component makers' rpm ratings govern.
• Horsepower from Quarter-Mile Trap Speed - The dyno-free power check a racer runs off the timeslip: Hale's HP = weight x (mph/234)^3 inverts the quarter-mile trap speed to horsepower. A 3,200 lb car trapping 108 mph made 315 hp at the wheels (companion ET 12.6 s); a 7 mph faster trap (115 mph) implies 380 hp, a 20% jump - the cube law that makes trap speed, not ET, the cleaner power indicator. Empirical fit to typical cars, wheel power, not a substitute for a dyno. A hobbyist estimate; the actual dyno measurement governs.
• Horsepower from Quarter-Mile ET - Horsepower from the quarter-mile elapsed time, the ET companion of the trap-speed tile: HP = weight x (5.825/ET)^3 inverts Hale's ET relation. A 3,200 lb car running a 12.63 s quarter made ~314 hp; a quicker 11.5 s ET implies ~416 hp - the cube law. ET is what a timeslip gives directly, but it is corrupted by traction and the launch (spin or bog runs a slower ET at the same power), so trap speed is the cleaner indicator when available. Empirical fit, wheel power, not a dyno. A hobbyist estimate; the dyno governs.
• 2K Paint Mix Ratio - The hardener and reducer to add and the total batch from a ratio like 4:1 or 4:1:1 and a measured base-paint volume, in fluid ounces and milliliters. Ratios are by volume.
• Hydraulic Pump Drive Horsepower - Fluid HP = gpm x psi / 1714, drive HP = fluid HP / efficiency. 10 GPM at 2000 psi, 0.85 efficiency -> 11.7 fluid HP, 13.7 drive HP (size the motor to 13.7 and round up); at 100% efficiency the 2.0 HP gap is the pump loss. A sizing aid; the pump and motor data govern.
• Hydraulic Flow Limit from Drive Power - The inverse of the hydraulic-pump-horsepower tile: the most flow a power unit can deliver at a working pressure for a given drive horsepower, gpm = 1714 x drive_hp x efficiency / psi. A 13.7 HP drive at 2,000 psi and 0.85 efficiency moves 10 GPM; raise the pressure to 3,000 psi and it drops to 6.7 GPM (flow trades against pressure at fixed power). Answers 'how much flow can this motor drive' instead of the HP for one flow. A power ceiling, not the pump's rated flow. The pump and motor data govern.
• Hydraulic Motor Torque and Speed - Torque = psi x disp / (2 pi) x mech eff, speed = 231 x gpm / disp x vol eff, HP = T x rpm / 63025. 2000 psi, 2.0 in^3/rev, 10 GPM -> 573 in-lb, 1097 rpm, 9.98 HP; doubling displacement halves speed and doubles torque (same power). A sizing aid; the motor data govern.
• Hydraulic Pump Output Flow - The gpm a pump delivers from its displacement and drive speed - the inverse of the hydraulic-motor speed relation and the flow the pump-horsepower tile takes as input: theoretical flow = disp x rpm / 231, delivered = theoretical x volumetric efficiency. A 2.0 in^3/rev pump at 1800 rpm and 0.95 vol eff makes 15.58 theoretical but delivers 14.81 gpm - the 0.78 gpm difference is internal slip that grows with pressure and wear. A sizing aid; the pump manufacturer's data govern.
• Cooling-System Coolant Flow for a Heat Load - gpm = Q / (c x deltaT), c = 500 water / 427 glycol. 150,000 Btu/hr at a 10 F rise needs 30 GPM (water) or 35 GPM (50/50 glycol, ~17% more); a tighter 5 F rise doubles the flow to 60 GPM. A sizing aid; the equipment ratings and fluid properties govern.
• Marine Propeller Pitch Selection - The pitch to swap to so the engine reaches the top of its rated RPM band at wide-open throttle: each inch of pitch changes WOT RPM by ~200 rpm, so pitch change = (target - current WOT RPM) / rpm-per-inch and new pitch = current - change. A 19 in prop hitting 5000 rpm against a 5400 target drops to a 17 in prop; a boat over-revving to 6000 goes up to 22 in. Under-rev needs less pitch, over-rev needs more. A selection aid; a WOT test with the new prop and the dealer's prop chart govern.
• Engine Fuel Burn from Horsepower (BSFC) - The fuel burn in gallons per hour from engine power and brake-specific fuel consumption: lb/hr = HP x BSFC, gph = lb/hr / fuel density (diesel ~7.1, gasoline ~6.1 lb/gal), and run time = tank / gph. A 300 hp diesel at BSFC 0.37 burns 15.6 GPH (12.8 hours on a 200 gal tank); the same power from a gasoline engine (BSFC 0.50) burns 24.6 GPH, 58% more. The burn at the entered power; real duty-cycle burn is lower. A planning aid; the engine's fuel map and a measured burn govern.
• Chamber Volume for a Target Compression Ratio - The inverse of the displacement-cr tile: the combustion-chamber volume needed to hit a target static compression ratio, TDC_volume = cylinder_cc / (target_CR - 1) and chamber = TDC_volume - gasket - deck + dome. A 4.0 x 3.48 in cylinder (716.7 cc) targeting 10.73:1 needs a 64 cc chamber; drop the target and the chamber grows. Tells you how much to mill the head or how large a dished/domed piston to run for a target CR, instead of the CR from one chamber. Static CR only; cc'ing the actual chambers governs.
• Screw Conveyor Speed for a Target Capacity - The inverse of the screw-conveyor tile: the auger speed needed to hit a target volumetric capacity, rpm = target_ft3_hr / (flight_area x (pitch/12) x 60 x loading) (CEMA Book No. 350). A 9 in screw with a 2.5 in shaft, 9 in pitch, at 30% loading needs 40 RPM for 220 ft^3/hr; double the target and it needs 80 RPM (capacity is linear in speed). Divide a mass rate by the bulk density for the volumetric target first. A flagged high RPM means step up a screw size. CEMA and the manufacturer govern.
• Helical Compression Spring Rate - The stiffness of a coil spring from its wire and coil geometry: k = G d^4 / (8 D^3 Na), G the wire shear modulus by material, d the wire diameter, D the mean coil diameter (OD - d), Na the active coils. A 0.080 in hard-drawn wire, 0.75 in mean coil, 8 active coils is 17.4 lb/in (spring index 9.4). Get Na from total coils by end condition (squared-and-ground Nt - 2). A good index D/d is 4-12. Rate only, not stress or solid height; Machinery's Handbook / Shigley, the spring maker governs.
• Driveshaft Max Length for an Operating Speed - The inverse of the driveshaft-crit tile: the longest a tube can be before it whips at a target operating speed, L_max = L_ref x sqrt(0.65 x N_crit_ref / target_rpm), since the first-mode critical speed falls as 1/length^2 and you stay below 0.65 of critical. A 3.5 in x 0.083 in steel tube running at its 2,800 RPM safe limit maxes at 50 in; halve the RPM and it can grow 41% to 71 in. Answers 'how long can I make it' instead of the critical speed of one length. A bare-tube estimate; split a long run with a center bearing. The driveline manufacturer governs.
• Alternator Charging Load Balance - Whether the alternator keeps up with the electrical load at idle and cruise: it makes only ~50% of its rated output at idle and ~90% at cruise, so balance = output - total continuous load. A 65 A load on a 120 A alternator runs a 5 A deficit at idle (battery drains at stoplights) but a healthy +43 A at cruise; a 160 A alternator turns the idle balance to +15 A. A screening aid; the alternator's actual output curve and the real duty cycle govern.
• Torque Wrench Extension / Crowfoot Correction - The wrench setting a crowfoot or in-line extension demands, which bolt-torque never gives: TW = TA x L / (L + E cos(angle)), the target torque scaled by the wrench lever L over the lengthened lever. A 3 in in-line crowfoot on an 18 in wrench targeting 100 ft-lb means dialing 85.7 - set it to 100 instead and you apply 116.7 ft-lb, a 17% over-torque that snaps small fasteners. Swing the crowfoot to 90 degrees and cos goes to zero, so no correction is needed - the field workaround. A shop aid; the calibrated wrench and the manufacturer's torque spec govern.
• Density Altitude and Pressure Altitude - Why a 5,000 ft strip flies like 8,500 ft on a hot day: the FAA density-altitude method turns field elevation, altimeter setting, and temperature into the performance altitude a chart is entered with. PA = elevation + (29.92 - altimeter) x 1000; ISA = 15 - 2 x (PA/1000) C; DA = PA + 120 x (OAT - ISA). A 5,000 ft field at 29.92 and 95 F is 30 C warmer than standard -> DA 8,600 ft, so lift, engine power, and prop thrust all fall as if 3,600 ft higher; a cold -5 F day drops DA to about 1,930 ft, the winter bonus. Dry-air model (humidity lowers density further); the aircraft flight manual and the pilot in command govern.
• Crosswind and Headwind Component - The wind split pilots misjudge, and the gust that actually counts: angle = |wind dir - runway heading| folded to 0-180, crosswind = speed x sin(angle), headwind = speed x cos(angle). A wind '20 kt, 30 deg off' is only 10 kt of crosswind but 17 kt of headwind. Two traps made explicit: the value checked against the aircraft's maximum demonstrated crosswind is the GUST, not the steady wind, and a wind more than 90 deg off the nose becomes a TAILWIND -- it still adds crosswind while erasing the headwind margin, the setup that overruns a runway. Returns both components with a tailwind flag and a demonstrated-crosswind check. A planning aid; the pilot in command and the flight manual govern.
• Displacement Hull Speed and Speed/Length Ratio - The displacement wall horsepower cannot push through: a displacement hull is trapped by the wave it makes, so hull_speed = 1.34 x sqrt(LWL) knots is a hard ceiling. A 25 ft waterline caps near 6.70 kn no matter the power, until a planing hull breaks free. Enter an actual speed for the speed-length ratio SL = speed / sqrt(LWL) and the regime: SL <= 1.34 displacement, 1.34-2.5 semi-displacement, > 2.5 planing (that same 25 ft hull at 18 kn is SL 3.6, planing, off the wall). A boater reading a prop-based speed without the displacement wall over-predicts a heavy cruiser and over-props the engine. A planning estimate; the hull form, displacement, and power govern.
• Hull Displacement and Block Coefficient - A boat's displacement -- what it weighs, since by Archimedes it floats on the weight of water it pushes aside. The immersed L x B x draft box is filled only partway by the real hull shape, that fraction being the block coefficient Cb (~0.35-0.45 fine/planing, 0.40-0.60 full/work hull). Displacement volume = LWL x BWL x draft x Cb; weight = volume x water density (64.0 lb/ft^3 seawater, 62.4 fresh); long tons = weight/2,240. A 30 ft waterline, 10 ft beam, 4 ft draft hull at Cb 0.5 in seawater displaces 600 ft^3 = 38,400 lb = 17.1 long tons; fresh water floats it a touch deeper. A first-order block estimate for sizing ground tackle, a trailer, or a lift; the lines drawing integrated by Simpson's rule (or the builder's displacement table), the loaded trim, and the naval architect's hydrostatics govern the real value.
• Waterline Length for a Target Hull Speed - The inverse of the hull-speed tile: the waterline a pure displacement hull needs to reach a target speed, LWL = (target speed / 1.34)^2. An 8 kn displacement cruiser needs a ~35.6 ft waterline; 12 kn needs ~80 ft. This is the displacement ceiling - a planing hull breaks free with enough power. The coefficient is editable (~1.34-1.4). A planning estimate; the hull form, displacement, and power govern.
• Anchor Rode Scope and Swing Radius - The bow-height-and-high-tide scope that keeps an anchor set: scope is rode paid out over the VERTICAL rise from the seabed to the bow roller -- depth PLUS bow-roller height, at HIGH tide, not the sounder depth. In 15 ft of water with a 3 ft bow roller the true vertical is 18 ft, so a 7:1 scope needs 126 ft of rode (a 154.7 ft swing radius for a 30 ft boat); anchoring on 15 ft alone pays out only 105 ft = an actual 5.8:1, the quiet error that drags at 2 a.m. All-chain holds at 3:1 (54 ft rode, an 80.9 ft swing) -- a tighter circle, why it is favored in a crowded anchorage. A planning aid; conditions, bottom type, and skipper judgment govern.
• Turbocharger Pressure Ratio and Charge-Air Temp - Why boost is a gauge number and why it needs an intercooler: PR = (ambient_abs + boost) / ambient_abs, so the ambient must be added before dividing -- 15 psi at sea level (14.7 psia) is PR 2.02, but the same 15 psi a mile high (12.2 psia) is PR 2.23, a hotter outlet for the identical boost. Compressing air heats it: T_out = T_in x [1 + (PR^0.283 - 1)/efficiency], so 15 psi at 80 F inlet and 70% efficiency reaches 250 F -- a 170 F rise from compression alone, why an intercooler is mandatory on a serious build. Reports the compressor-outlet (not manifold) temperature. A planning estimate; the compressor map and engine build govern.
• Max Boost Before a Charge-Air Temperature Limit - The inverse of the turbo pressure-ratio tile: the gauge boost at which the compressor-outlet charge-air temperature reaches a limit, boost = ambient x ([1 + eff x (T_out/T_in - 1)]^(1/0.283) - 1). An 80 F inlet, 70% compressor, 250 F limit tops out near 15 psi; a more efficient compressor or a cooler inlet buys more. Compressor-outlet temp (ignores intercooling). A planning estimate; the compressor map and engine build govern.
• Crouch Planing-Speed Estimate - The planing top-speed estimate and its diminishing return, the opposite regime from the displacement hull-speed wall: Crouch's formula speed = C / sqrt(weight / hp), in MILES PER HOUR (not knots), with the hull constant C about 150 heavy cruiser, 190 runabout, 210 race. A 6,000 lb runabout with 200 hp and C = 190 makes 34.7 mph; double the power to 400 hp and it reaches only 49.1 mph -- twice the horsepower buys sqrt(2) = 41% more speed, not double, because speed scales with the square root of the power-to-weight ratio. Assumes the boat is on plane (below the planing threshold use the hull-speed tile). A planning estimate; the hull, propeller, and conditions govern.
• Horsepower for a Target Planing Speed - The inverse of the crouch-planing-speed tile: the shaft horsepower Crouch's formula says a planing hull needs to hit a target speed, hp = weight x (speed / C)^2 (speed in MILES PER HOUR, not knots; C about 150 cruiser, 190 runabout, 210 race). A 6,000 lb runabout targeting 34.7 mph at C = 190 needs 200 hp; to reach 49.1 mph it needs about 400 hp -- horsepower rises with the SQUARE of the target speed, so 40% more speed roughly doubles the power. Assumes the boat is on plane. A planning estimate; the hull, propeller, and conditions govern.
• Wheel Offset and Backspacing - Converting wheel offset to backspacing, and where the inch hides: offset (ET, mm, mounting face to centerline) and backspacing (in, mounting face to inboard rim edge) describe the same fitment in different units. backspacing = rim_width/2 + 0.5 + offset/25.4, and the rim 'width' is the bead seat -- the wheel is ~1 in wider overall (half an inch per flange), the omission that makes a fitment come out an inch wrong. An 8 in wheel at +45 mm has 6.27 in backspacing and 2.73 in frontspacing; a zero-offset wheel sits nearly 1.8 in further out. A more positive offset pulls the wheel inboard (more fender, less brake/strut clearance). A fitment aid; the wheel, hub, and suspension clearances govern.
• Brake Pedal Ratio and Line Pressure - Why doubling the master-cylinder bore quarters the pressure: Pascal's law end to end. mc_force = pedal x ratio x booster; line pressure = mc_force / (pi/4 x bore^2); clamp = line pressure x caliper area; brake torque = clamp x 2 x friction x rotor radius. A 50 lb pedal at 5:1 manual through a 7/8 in master makes 416 psi -> 1,663 lb clamp -> 5,987 in-lb per corner; swap to a 1.75 in master (double the bore) and the pressure drops to 104 psi, exactly a quarter, for the same leg -- the whole manual-vs-boosted trade. The 2 in the torque is both pad faces. A design aid; the pad friction, thermal state, and system compliance govern.
• SAE J1349 Dyno Correction Factor - The dry-pressure correction that makes two dyno pulls comparable: SAE J1349 corrects observed power to a standard day (25 C, 99 kPa DRY). The catch is 'dry' -- subtract the water-vapor pressure from the barometric before applying, because humid air makes less power. P_dry = baro - vapor; CF = 1.18 x (990/P_dry) x sqrt((T+273)/298) - 0.18; corrected = observed x CF. 400 hp at 980 mbar dry, 30 C -> CF 1.0220 -> 408.8 hp; a hotter, thinner 970 mbar / 35 C day corrects harder, CF 1.0444. Valid only ~15-35 C, 900-1050 mbar (flagged outside); the older STD (J607) basis runs ~4% higher and cannot be compared to SAE. A comparison aid; the dyno and correction basis govern.
• Aircraft Weight and Balance (CG Envelope) - The in-gross-weight-but-out-of-CG load weight-and-balance exists to catch: sum the station moments (empty, occupants, fuel, baggage), CG = total moment / total weight, legal only if weight <= max gross AND fwd_limit <= CG <= aft_limit. A 1,500 lb (39 in) aircraft with 340 lb front, 180 lb fuel, 200 lb baggage is 2,220 lb, CG 44.47 in -- legal. Fly lighter but pack 300 lb of baggage aft and it is 2,100 lb (under gross) yet CG 47.24 in -- BEHIND the 47 in aft limit and dangerously unstable. Fuel burn moves the CG, so both takeoff and landing CG must be in the envelope. A loading aid; the aircraft flight manual and the pilot in command govern.
• ABYC E-11 Marine DC Wire Sizing - Why a dockside NEC wire size undersizes on a boat: ABYC E-11 sizes on the ROUND-TRIP length (out and back), CM = 10.75 x current x (2 x length) / V_drop, not the NEC one-way habit -- and the marine allowable drop is stricter where it matters, 3% for panelboard feeders and nav/critical loads (10% non-critical). A 20 A nav feeder, 25 ft one-way, 12 V, 3% has only 0.36 V of headroom -> 29,861 circular mils -> #4 wire (#6 falls short); relax to 10% non-critical and it drops to 8,958 CM -> #10, three sizes smaller. The ABYC ampacity table sets a separate floor the drop size must clear. A design aid; the standard, wire temperature rating, and installation govern.
• Cutting-Fluid Concentration - The running concentration of a coolant sump from a refractometer Brix reading and the fluid's factor, and the concentrate to add (or water to add) to bring it to a target.
• Battery Reserve Capacity to Amp-Hours - The amp-hours behind a battery's reserve-capacity minutes: BCI / SAE J537 reserve capacity is the minutes a fully charged 12 V battery at 80 F sustains a 25 A draw to a 10.5 V cutoff, so amp-hours at that rate = 25 x RC/60 -- an RC of 120 minutes is 50 Ah. This RC-rate capacity is lower than the 20-hour-rate amp-hours on a deep-cycle label (Peukert's effect), so the two are not interchangeable; cold reduces it further. A comparison aid; the battery rating and a load test govern.
• Sacrificial Anode Service Life - How long a boat's zinc, aluminum, or magnesium anode lasts, by Faraday's law: life = anode mass x electrochemical capacity x utilization / (protective current x 8760 h). A 5 lb zinc (354 A-h/lb) at 0.85 utilization drawing 0.15 A lasts about 1.1 years -- the annual haul-out replacement. Aluminum (Al-Zn-In, ~1150 A-h/lb) of equal mass lasts far longer per amp and works in brackish water where zinc passivates, which is why it has largely replaced zinc. The protective current depends on wetted area, coating, and water; measure it with a reference electrode. Replace at about half consumed. A planning estimate; ABYC E-2 and a corrosion survey govern.
• Engine BMEP (Brake Mean Effective Pressure) - Torque normalized by displacement, so engines of any size compare directly on how hard each cycle works: BMEP = 150.8 x torque(lb-ft) / displacement(CID) for a 4-stroke (75.4 for a 2-stroke). A 350 CID V8 at 400 lb-ft runs 172 psi -- squarely in the healthy naturally-aspirated gasoline range. NA gas engines top out near 180-190 psi because they fill on one atmosphere, so a BMEP above that is the signature of boost, and a low value points to a mild cam, a restriction, or wear. Evaluated at the torque peak from a corrected dyno pull. A comparison metric, not a design limit; the dyno sheet governs.
• Glidepath Rate of Descent - The rate of descent that holds a glidepath, from the ground speed: ROD = ground speed x 101.27 x tan(angle) ft/min, and the path itself is 6076.12 x tan(angle) ft/nm -- 318 ft/nm at a standard 3.00 degree ILS, the exact FAA TERPS figure that fixes the tangent form. At 120 kt on a 3-degree path that is 637 ft/min, which the 'ground speed x 5' rule rounds to 600. Because it scales with GROUND speed, a tailwind or a faster approach demands a higher descent rate to stay on the same path. A planning aid, not a clearance; the approach chart and the pilot in command govern.
• Coordinated Turn Radius and Rate - The radius and rate of a coordinated level turn from airspeed and bank: tan(bank) = V^2/(g x radius), so radius = 0.08854 x airspeed(kt)^2 / tan(bank) -- depending only on speed and bank, not weight or aircraft type. At 120 kt and 30 degrees the radius is about 2,208 ft (0.36 nm) at 5.25 deg/s. Speed enters squared, so doubling it quadruples the radius, which is why a fast jet needs miles to turn while a trainer needs yards; a standard-rate turn is 3 deg/s (a 2-minute 360). Level coordinated flight assumed. A planning aid; the flight manual and the pilot in command govern.
• Climb Gradient to Rate of Climb - Reconciles a departure's climb GRADIENT (feet per nautical mile, the obstacle-clearance slope) with the cockpit rate of climb (feet per minute) through the ground speed: ROC = gradient x ground speed / 60. A 300 ft/nm gradient at 120 kt needs 600 ft/min; the gradient as a percent is ft/nm over 6076.12 (the 200 ft/nm default is ~3.3%). The trap: because it scales with GROUND speed, flying faster or a tailwind demands a HIGHER rate of climb for the same gradient, and a heavy, high-density-altitude departure may not make a steep gradient at all -- the takeoff go/no-go. A planning aid; the departure procedure and performance charts govern.
• Cutting Power and Spindle Torque - Cutting horsepower, motor horsepower after drive efficiency, and spindle torque from the material removal rate and the specific cutting energy (unit power: about 1.0 carbon steel, 0.33 aluminum, 1.5 stainless/titanium) -- the stall / motor-size check before a heavy cut. The tool and machine govern the real draw.
• Max Material Removal Rate from Spindle Power - The inverse of the cutting-power tile: the power-limited max removal rate a spindle can drive, max MRR = motor hp x efficiency / unit power. A 5 hp spindle at 80% efficiency removes up to 4.0 in3/min of carbon steel (unit power 1.0), or 12.1 in3/min of aluminum (0.33). The stall limit only -- depth/feed, tool strength, and rigidity are separate. The tool and machine govern the real cut.