Delta-V & Gravity Drag
Learning Objectives
- Identify why flying vertically for too long wastes Delta-V ($\Delta v$).
- Define the aerodynamic penalty known as Gravity Drag.
- Conclude perfectly why a "Gravity Turn" arc is the mathematical middle ground between atmospheric death and gravitational bankruptcy.
We know we must fly vertically to escape the atmosphere (Max-Q). So why don't rockets just fly vertically all the way up to $400\text{ km}$, stop, and *then* fire horizontally?
1.5.5 The Cost of Fighting Gravity
Every single second your rocket engine is pointed directly at the ground fighting gravity, it is burning precious chemical fuel that is NOT being used to build your $7.6\text{ km/s}$ horizontal orbital speed.
Earth's gravity constantly accelerates downward at $9.81\text{ ms}^{-2}$. Therefore, if you aim your rocket straight up for $100$ seconds, gravity will literally steal $981\text{ m/s}$ of your hard-earned velocity. This invisible, relentless theft of your rocket's velocity is known as Gravity Drag.
The $\Delta v$ Budget
A rocket's gas tank is measured confusingly but brilliantly in Velocity ($\Delta v$). If your rocket has a $\Delta v$ budget of $10\text{ km/s}$, you will spend roughly $1.5\text{ km/s}$ of it purely fighting Gravity Drag. You want this tax to be as small as possible!
1.5.6 The Perfect Compromise
Here we arrive at the absolute pinnacle of early aerospace engineering. The flight computer is trapped in a paradox:
- If you pitch horizontally too early, you hit the wall of the atmosphere and instantly explode from Max-Q.
- If you pitch horizontally too late, you waste millions of Joules hovering vertically, allowing Gravity Drag to drain your fuel tanks until you crash.
FIGURE 5.2: THE GRAVITY TURN
The solution is a smooth parabolic curve. You lift vertically to escape the thickest air, then gently pitch a few degrees over. Gravity then slowly pulls the rocket's velocity vector downward naturally as it climbs. By the time it hits the vacuum of space, it is coasting perfectly horizontally.