formula.expert

Engine out: how far can you glide

Flight mechanics · the drag polar to the glide ring

A light single loses its engine at 2,000 m above flat terrain and settles onto best-glide speed, where the dynamic pressure is 1,800 Pa. The wing's reference area is 16.2 m², the zero-lift drag coefficient is 0.025, and at this speed the induced drag coefficient is 0.018. The aircraft weighs about 11,300 N, which in a steady glide is what the lift must carry. Find the total drag coefficient, the drag force, the lift-to-drag ratio, and the distance the height can buy.

hLDWC_D0C_Di1 : L/Dxlanding field

Every number in this problem is editable — change any value below and the whole chain recalculates.

Given
  • C_D0 = 0.025 — — Zero-lift drag coefficient
  • C_Di = 0.018 — — Induced drag coefficient at best glide
  • q = 1,800 Pa — Dynamic pressure at best glide
  • S = 16.2 m² — Wing reference area
  • L = 11,300 N — Lift ≈ weight in the glide
  • h = 2,000 m — Height above terrain
Determine
  1. (a)the total drag coefficient
  2. (b)the drag force at best glide
  3. (c)the lift-to-drag ratio
  4. (d)the glide distance
Step 1 of 4(a) · solve for Total drag coefficient

The polar splits drag into the part you pay for existing — skin, rivets, antennas — and the part you pay for lifting. At best glide the two are the same order on purpose: 0.025 and 0.018 sum to 0.043, near the point where their trade-off bottoms out.

VCDCD0CDiCD
Rearranged for C_D
CD=CD0+CDiC_D = C_{D0} + C_{Di}
Your values, in your units
CD=(0.025)+(0.018)C_D = \left( 0.025 \right) + \left( 0.018 \right)
Answer
CD=0.043C_D = 0.043

Carried onward at full precision, not this rounded figure.

Open the Drag Polar solver →

Step 2 of 4(b) · solve for Drag force

The coefficient becomes a force through qS: 1,800 Pa over 16.2 m² of reference wing at C_D 0.043 is 1,254 N of drag — the thrust the propeller is no longer supplying, now paid for in altitude instead.

qDS
Rearranged for D
D=q S CDD = q \, S \, C_D
0.043 carried from step 1
Your values, in your units
D=(1,800 Pa)⋅(16.2 m2)⋅(0.043)D = \left( 1{,}800\ \text{Pa} \right) \cdot \left( 16.2\ \text{m}^{2} \right) \cdot \left( 0.043 \right)
Answer
D=1.2539 kND = 1.2539\ \text{kN}

Carried onward at full precision, not this rounded figure.

Open the Drag Equation from the Drag Coefficient solver →

Step 3 of 4(c) · solve for Lift-to-drag ratio

With lift pinned to weight, L/D is the machine's honesty about itself: 11,300 N carried for 1,254 N spent is 9.0 — every metre surrendered moves the aircraft nine forward. This is the number the flight manual calls glide ratio.

LDL/D
Rearranged for L/D
L/D=LDL/D = \frac{L}{D}
1.2539 kNcarried from step 2
Your values, in your units
L/D=(11,300 N)(1,253.88 N)L/D = \frac{\left( 11{,}300\ \text{N} \right)}{\left( 1{,}253.88\ \text{N} \right)}
Answer
L/D=9.012L/D = 9.012

Carried onward at full precision, not this rounded figure.

Open the Lift-to-Drag Ratio solver →

Step 4 of 4(d) · solve for Glide distance

Height times L/D: 2,000 m buys 18.0 km of still-air reach — a circle 36 km across to find a field in. Wind moves the circle without growing it, and stretching the glide by raising the nose shrinks it: below best-glide speed, induced drag climbs and the ratio collapses.

hxL/D
Rearranged for x
x=h⋅LDx = h \cdot \frac{L}{D}
9.012 —carried from step 3
Your values, in your units
x=(2,000 m)⋅(9.01203)x = \left( 2{,}000\ \text{m} \right) \cdot \left( 9.01203 \right)
Answer
x=18.024 kmx = 18.024\ \text{km}

Carried onward at full precision, not this rounded figure.

Open the Glide Distance from Altitude solver →

Answer

Therefore C_D = 0.043, the drag at best glide is 1,254 N, the lift-to-drag ratio is 9.0, and two thousand metres of height is eighteen kilometres of reach — provided the nose is held at best-glide speed and nowhere kinder.

Why this order

The chain runs from aerodynamic bookkeeping to a life-sized answer. The polar's split matters because the two parts move opposite ways with speed: parasite drag grows with q, induced drag shrinks with it, and best glide is the speed where their sum bottoms — which is also, not coincidentally, where L/D peaks. That is why the glide ratio is a property of the airframe and not of the day: weight changes the best-glide SPEED, but barely touches the ratio, so a heavy aircraft glides just as far, faster.

The killing mistake this chain exists to argue against is stretching: the instinct to raise the nose when the field looks far. Below best-glide speed the induced term takes over, L/D falls, and the aircraft comes down more steeply while pointing more hopefully — the picture improves as the physics worsens. The discipline is one number: hold the speed, accept the ring it draws, and choose inside it.

Carried values move at full precision, not the rounded figure shown — chaining rounded numbers compounds error.