14.1 Virtual/Resultant Condition and Bonus Formulas

14.1 Virtual/Resultant Condition and Bonus Formulas

Quick Answer: The virtual condition (VC) is the worst-case mating boundary a feature can present to its mate: external VC = MMC + position tolerance, internal VC = MMC − position tolerance. The resultant condition (RC) is the opposite boundary: external RC = LMC − (position tol + bonus), internal RC = LMC + (position tol + bonus). Bonus = |actual size − MMC| and is only available when the position control is applied at MMC.

Why VC and RC matter

Every feature of size controlled with a position, profile, or orientation tolerance at MMC generates two extreme boundaries. The virtual condition is the boundary used for assembly verification (and for functional GO gaging); the resultant condition is the boundary used to check minimum wall thickness, edge distance, and the LMC-side limit. On the Senior exam, almost every location or datum-shift calculation reduces to evaluating VC, RC, or bonus, so the sign convention must be automatic.

The master formulas

A useful mnemonic: external adds, internal subtracts for VC; the reverse sign appears on RC. The bonus is always the absolute departure from MMC and is zero at MMC and maximum at LMC.

Worked example — external pin

A pin is dimensioned Ø10 ± 0.2 with position Ø0.1 at MMC to datums A|B|C.

• MMC = 10.2, LMC = 9.8, size tolerance = 0.4.
• VC = MMC + pos tol = 10.2 + 0.1 = Ø10.3 (the mating hole must clear Ø10.3).
• At an actual pin size of Ø10.0: bonus = |10.0 − 10.2| = 0.2, so total position tolerance = 0.1 + 0.2 = Ø0.3.
• RC (worst, at LMC with full bonus) = LMC − (pos tol + max bonus) = 9.8 − (0.1 + 0.4) = Ø9.3 (the smallest inner boundary the pin can leave in the part).

The pin's surface must always lie entirely between Ø9.3 (RC inner) and Ø10.3 (VC outer). Any measured pin inside that envelope passes.

Worked example — internal hole

A hole is dimensioned Ø10 ± 0.2 with position Ø0.1 at MMC to datums A|B|C.

• MMC = 9.8 (smallest hole), LMC = 10.2 (largest hole), size tolerance = 0.4.
• VC = MMC − pos tol = 9.8 − 0.1 = Ø9.7 (a mating pin Ø9.7 will assemble in the worst case — this is the GO gage pin).
• At an actual hole size of Ø10.0: bonus = |10.0 − 9.8| = 0.2, total position tolerance = 0.1 + 0.2 = Ø0.3.
• RC (worst, at LMC with full bonus) = LMC + (pos tol + max bonus) = 10.2 + (0.1 + 0.4) = Ø10.7 (the largest outer boundary the hole can occupy — used for minimum wall checks).

Common traps

1. Sign error on RC. Candidates write RC = LMC ± pos tol without the bonus. RC always includes the maximum bonus (the full size tolerance) when evaluated at LMC.
2. Confusing bonus with datum shift. Bonus is per-feature and grows as that one feature departs from MMC. Datum shift moves the entire datum reference frame; it is not a per-feature bonus (covered in 14.2).
3. Applying bonus at RFS. If the position frame has no MMC modifier, the default per Y14.5-2009 is RFS, and bonus = 0. You cannot add a bonus just because the feature has a size tolerance.
4. Mixing radial/diametral. Position zones are stated as diameters; bonus is also a diameter. When computing a wall-thickness limit, divide the relevant diameters by 2 to use radial values.
5. Using MMC for an LMC-controlled feature. When the modifier is LMC, swap the roles: bonus = |actual − LMC|, and the functional boundary is the LMC-derived one (often the inner boundary for a hole, used to guarantee minimum material / clearance for a casting).

Senior exam payoff

Roughly a third of the 150 Senior questions involve a calculation or boundary judgment. If you can compute VC, RC, and bonus in under 30 seconds for any feature of size, you have the arithmetic backbone for the Location (25%), Datum (30%), and many Profile (20%) questions. Practice with the table above until the signs are automatic.