If TAS at sea level is 110 knots, what is TAS at 4,000' density altitude?

If TAS at sea level is 110 knots, what is TAS at 4,000' density altitude?

• A. 110 knots
• B. 118.8 knots
• C. 120 knots
• D. 132 knots

Answer: (B)

Density altitude changes air density, and true airspeed rises for a given indicated airspeed when the air is thinner. For a fixed IAS, TAS scales with the square root of the density ratio: TAS ≈ IAS × sqrt(ρ0/ρ). At 4,000 feet density altitude, air density is lower than at sea level—about 0.857 of sea level density. So the factor is sqrt(1/0.857) ≈ 1.08. With a sea-level TAS of 110 knots, the true airspeed becomes roughly 110 × 1.08 ≈ 118.8 knots. The other values would require either no change or a much larger density drop than 4,000 feet DA provides, so they don’t fit standard atmosphere conditions.

Density altitude changes air density, and true airspeed rises for a given indicated airspeed when the air is thinner. For a fixed IAS, TAS scales with the square root of the density ratio: TAS ≈ IAS × sqrt(ρ0/ρ). At 4,000 feet density altitude, air density is lower than at sea level—about 0.857 of sea level density. So the factor is sqrt(1/0.857) ≈ 1.08. With a sea-level TAS of 110 knots, the true airspeed becomes roughly 110 × 1.08 ≈ 118.8 knots. The other values would require either no change or a much larger density drop than 4,000 feet DA provides, so they don’t fit standard atmosphere conditions.