When evaluating the feasibility of launching a high-velocity projectile directly into space, one of the main objections is that the lower atmosphere is simply too dense—producing extreme dynamic pressures and intolerable aerodynamic heating. At sea level, the air density is so high that a vehicle traveling at 11 km/s would encounter heating rates beyond the capacity of any practical thermal management system. Conversely, at very high altitudes (above about 50–60 km), the atmosphere is thin enough, and the duration of atmospheric transit is short enough, that aerodynamic heating becomes a minor or even negligible concern.

The purpose of this claim is to assert that at an altitude of approximately 15 km, the air density is sufficiently low to limit both dynamic pressure and convective heating to levels that can be managed through short-duration active cooling. This altitude represents a practical compromise between two competing engineering challenges: designing the vehicle’s thermal management system to withstand higher heat fluxes at lower altitudes, or extending the elevated evacuated launch tube to much greater altitudes where such heating would no longer be significant. The 15 km regime is thus identified as a technically demanding but feasible operating point—one that can be achieved with available materials and proven engineering techniques, without requiring any breakthroughs in science or technology.

When a vehicle exits the elevated evacuated tube at an altitude of 15 km, its speed in the inertial reference frame will be 11,546 m/s, but because the Earth is rotating in the same direction as the vehicle's travel, its airspeed will be 11,110 m/s. The air pressure at 15 km is 0.119 atm, and the air density is 0.192 kg/m³. Airspeed is maintained, but air density drops as the vehicle gains altitude. The following charts show results produced by the digital twin.

The vehicle design minimizes atmospheric drag with a long, slender nosecone that narrows to a hemispherical tip having a radius of 1mm.

Let's assume that the nosecone tip is fabricated from TZM molybdenum alloy, a refractory metal that combines very high-temperature capability with high thermal conductivity and mechanical strength. It retains a yield strength over 250 MPa at 1000–1200 °C, conducts heat at approximately 125 W m⁻¹ K⁻¹, and melts near 2620 °C. These properties make it ideal for withstanding brief, intense aerodynamic loads and spreading heat effectively—ensuring both structural and thermal integrity without requiring exotic materials.

Stagnation Dynamic Pressure

The first concern is dynamic pressure — the direct mechanical load from the airflow. It’s given by

$q = \tfrac{1}{2} \rho V^2 = \tfrac{1}{2}(0.192)(11110^2) = 1.185\times10^7\ \text{Pa} = 11.85\ \text{MPa}.$

For a small hemispherical TZM tip, the resulting membrane stress is

$\sigma = \dfrac{p\,r}{2t} = \dfrac{(11.85\times10^6)(0.001)}{2(0.0003)} = 19.8\ \text{MPa},$

well below the alloy’s yield strength of over 250 MPa at 1000 °C. In short, the structure easily withstands the aerodynamic load; the real challenge lies in managing the heat, not the pressure.

Convective Heating

The second concern is convective heating at the stagnation point — the intense thermal flux generated as air molecules are suddenly decelerated and compressed against the nose tip. It can be estimated using the relation

$q_{\text{conv}} = k\,\sqrt{\dfrac{\rho}{R_n}}\,V^{3},$

where $k = 1.83\times10^{-4}$ for air. Substituting the known values,

$q_{\text{conv}} = (1.83\times10^{-4})\sqrt{\dfrac{0.192}{0.001}}(11110)^3 = (1.83\times10^{-4})(13.856)(1.371\times10^{12}) = 3.47\times10^{9}\ \text{W/m}^2 = 3{,}474\ \text{W/mm}^2.$

Thus, the convective heating rate at the nose tip reaches about 3.47 kW per mm², an immense but brief heat flux that must be handled through active cooling during the few seconds of dense-air transit.

Radiative heating

The third concern is radiative heating from the hot, post-shock gas. A common misconception is that it scales like $V^8$ (from chaining $T\!\sim\!V^2$ with blackbody $\sigma T^4$). In real Earth-entry shock layers, nonequilibrium chemistry, line emission, and self-absorption flatten the dependence; in the 10–12 km/s band a practical fit is closer to $V^4$ and proportional to density:

$q_{\text{rad}} \approx C_{\text{rad}}\,\rho\,V^4.$

Using $C_{\text{rad}} = 2.0\times10^{-7}$...

$q_{\text{rad}} = (2.0\times10^{-7})(0.192)(11110)^4 = 5.8402\times10^{8}\ \text{W m}^{-2} = 584\ \text{W/mm}$

So, at 15 km and 11.11 km/s, radiation adds hundreds of W/mm² which is significant, but still below the convective peak; therefore both terms must be included in the nose-tip cooling budget.

Active Cooling with Pressurized Liquid Water

We remove the tip heat by circulating liquid water under high pressure (e.g., ~100 atm) through fine capillaries near the hot face, using sensible heating only (no boiling). The required mass flow is set by energy balance:

$\dot m = \dfrac{Q}{c_p\,\Delta T}.$

Tip heat load (1 mm radius hemisphere, area $A = 2\pi R^2 = 6.283\ \text{mm}^2$):

• Convective: $q_{\text{conv}} = 3{,}474\ \text{W/mm}^2 \Rightarrow P_{\text{conv}} = q_{\text{conv}}\,A = 21{,}830\ \text{W}.$
• Radiative: $q_{\text{rad}} = 584\ \text{W/mm}^2 \Rightarrow P_{\text{rad}} = q_{\text{rad}}\,A = 3{,}670\ \text{W}.$
• Total: $Q = P_{\text{conv}} + P_{\text{rad}} = 25{,}500\ \text{W}.$

With liquid water specific heat $c_p \approx 4.2\times10^3\ \text{J/(kg-K)}$ and a pressurized temperature rise $\Delta T \approx 275\ \text{K}$ (e.g., $25^\circ\text{C} \to 300^\circ\text{C}$, no flashing),

$c_p\Delta T \approx 1.16\times10^6\ \text{J/kg}.$

Thus,

$\dot m = \dfrac{25{,}500}{1.16\times10^6} \approx 2.20\times10^{-2}\ \text{kg/s}=22\ \text{g/s}.$

Heating drops from its peak to ~50% in the first 5 seconds, to ~10% after 10 seconds, and becomes negligible after around 25 seconds.

A TZM nose tip with an embedded network of micro-capillaries feeds cool water from a small reservoir, runs it within a few hundred microns of the hot surface, and returns it to the reservoir after absorbing heat. High pressure suppresses flashing, maintains liquid-phase properties (high $c_p$), and keeps the system compact. Only a few hundred grams of coolant are needed for the entire endoatmospheric transit.

Nose Cone Side-Wall Heating

Heating along the sides of the nosecone is far less significant than at the tip because the airflow there is nearly tangential and passes through an extremely weak oblique shock. With a half-angle of about 3.4°, the shock is only slightly stronger than the Mach wave, so post-shock temperature and density remain low. As a result, the local heat flux along the sidewall typically falls to less than 5–15% of the stagnation-point value, making the tip the overwhelmingly dominant source of aerodynamic heating.

Total Aerodynamic Drag Versus Rocket Thrust

The peak aerodynamic drag on the vehicle at 15km is 1,872,865 N, which is equivalent to 82% of one of the Space Shuttle's main engines (the RS-25). Rocket thrust is used briefly to offset aerodynamic drag and it is vectored as needed to adjust or maintain the spacecraft's flight trajectory.

Conclusion

• At 15 km, the dynamic pressure is mechanically tolerable for a refractory-metal nose; the governing risk is peak aerothermal load.
• Using a 1 mm tip with short-duration, pressurized, sensible-only water cooling at ~22 g/s (peak) and a micro-capillary network to move heat into a compact reservoir, the nose-tip heat can be removed throughout the brief high-q window.
• Because the heating decays by an order of magnitude within ~10 s and becomes negligible by ~25 s, the total coolant mass and system complexity remain modest, supporting the claim that a 15 km exit altitude enables safe endoatmospheric transit for this profile.
• The peak aerodynamic drag on the vehicle is low enough to be fully counteracted by a single liquid-fueled rocket engine.

See also: "Mass Driver Update", "The Era Of Earth-Based Mass Drivers" here.