Technical Trade SchoolBAS-100 foundation-series
BAS-107
Ten concept and evidence figures

BAS-107 Visual Aid Library

Figure-use rule

Each figure is an orientation and reasoning aid, not a project drawing. Learners must pair it with the current sequence, point list, wiring/piping documents, manufacturer instructions, and as-found evidence.

Figure 1 — Number sense, signs, fractions, decimals, percentages and estimation

Normal-rule anchor

The equation and units are part of the answer; extra decimal places do not create accuracy.

Case overlay

A calculator reports 2,400 percent damper position after a decimal is misplaced.

Calculation/evidence callout: Convert fractions/decimals/percent, calculate percent difference/change, round to justified precision, and bound results.

Figure 2 — Units, dimensions, prefixes and conversion factors critical

Normal-rule anchor

Never combine unlike units silently; squared and cubed conversions apply the factor more than once.

Case overlay

A duct area in square inches is entered as square feet without squaring the conversion factor.

Calculation/evidence callout: Convert common SI/IP quantities, C/F temperature, pressure and flow from supplied factors, with dimensional cancellation and reasonableness.

Figure 3 — Measurement, scales, drawings, geometry and quantities critical

Normal-rule anchor

Use written dimensions and verified scale correctly; sketches and screen zoom are not reliable measuring tools.

Case overlay

A 1/4-inch scale drawing is printed at 90 percent, changing every measured route.

Calculation/evidence callout: Calculate scaled distance, area/volume, right-triangle/rolling-offset geometry, quantities, allowances, and print-scale error.

Figure 4 — Algebra, equations, ratios, proportions and interpolation

Normal-rule anchor

Keep units attached while rearranging; a valid algebraic step can still violate the model domain or physical limits.

Case overlay

A linear reset equation is extrapolated beyond its defined outdoor-temperature range.

Calculation/evidence callout: Solve and rearrange one/two-step equations, ratios, slopes, interpolation, and clamp results to supplied limits.

Figure 5 — Electrical math: Ohm, power, VA, transformers and voltage drop critical

Normal-rule anchor

A steady-state voltage-drop answer is not full design proof when inrush, temperature, protection, or manufacturer minimums remain unknown.

Case overlay

Three actuators share a 24 Vac transformer and the farthest resets during simultaneous startup.

Calculation/evidence callout: Calculate current from VA/V, total VA, loop resistance, Vdrop=IR, delivered voltage, percent drop, spare capacity, and reasonableness.

Figure 6 — Signal scaling, calibration, error and engineering units critical

Normal-rule anchor

Correct arithmetic on the wrong range, unit, signal type, or reference is still wrong.

Case overlay

A 4-20 mA 0-250 Pa sensor is interpreted as 0-20 mA and displays a plausible error.

Calculation/evidence callout: Apply EU=LRV+(signal-livezero)/(span) x range, inverse scaling, percent span, offset/slope, and tolerance.

Figure 7 — HVAC math: airflow, heat, mixing, hydronics and efficiency critical

Normal-rule anchor

Shortcut constants embed assumptions about fluid and conditions; always state them and use project/engineering values when required.

Case overlay

A glycol loop is calculated with the standard water constant and appears to meet capacity.

Calculation/evidence callout: Calculate air/water heat, mixed air, ventilation fraction, unit conversions, load/capacity comparison, and reasonableness.

Figure 8 — Pressure, flow, fan/pump and proportional relationships critical

Normal-rule anchor

Proportional, square, and cube relationships have specific domains; device position is rarely equal to process flow.

Case overlay

A fan speed increases 10 percent and the learner predicts only 10 percent more power.

Calculation/evidence callout: Calculate square-root airflow, affinity-law examples, percent change, bounds, and compare predicted/observed response.

Figure 9 — Network math, binary/hex awareness, time and data rates critical

Normal-rule anchor

Address calculations support planning and diagnosis but do not authorize using unassigned addresses or changing owner networks.

Case overlay

A controller is assigned an address outside the VLAN subnet and trends fill storage faster after polling changes.

Calculation/evidence callout: Calculate subnet membership from supplied prefix, usable-count awareness, transmission/update time, samples/day, storage, and retention.

Figure 10 — Trends, averages, rates, tolerance, uncertainty and reasonableness; Integrated calculation record, error diagnosis and defense critical

Normal-rule anchor

An average can hide cycling and a correlation can hide sequence, mode, time, or secondary cause. The professional product is not a naked number; it is a reproducible decision record with limits and a reasonableness check.

Case overlay

Average zone temperature is acceptable, but five-minute oscillations create repeated complaints. Changed case: A spreadsheet gives convincing totals but uses feet as inches, one stale sensor value, and the wrong operating mode.

Calculation/evidence callout: Calculate average/median/range/rate, percent time outside band, missing data, combined tolerance awareness, and compare to physical limits. Recalculate independently, quantify error impact, reconcile all units/assumptions, and score calculation/record completeness.