Academics

This calculator outputs ambient pressure at a given altitude based on the 1962 US Standard Atmosphere. The partial pressure of oxygen in the alveolus uses the simplified alveolar gas equation with a partial pressure of H20 vapor of 47 mm Hg, a PaCO2 of 40, and a RQ of 0.8. This does not account for hypoxic changes in respiratory drive changing PaCO2.

FAA and FAR regulation for commercial aircraft pilots state that supplemental O2 is required for flights > 10,000 ft, 100% O2 is required for flights > 33,000 ft, and positive pressure breathing is required for flights > 40,000 ft. Pressure suits are required for flights > 50,000 ft. 

For more information on O2 systems from the FAA, click HERE.

The current US ISS spacesuit is pressurized to 226 mm Hg (0.3 bar) which is equivalent to 30,000 ft, and therefore require up to a 100% oxygen atmosphere in the suit to maintain PaO2 levels.

This calculator is designed to help demonstrate the effects of ascent through the atmosphere without supplemental oxygen (a constant 21% oxygen fraction). It calculates the ambient pressure based on the US standard atmosphere and the arterial partial pressure of oxygen based on the simplified alveolar gas equation (assumptions of a 47 mm Hg water vapor pressure, a PaCO2 of 40, and a RQ of 0.8) and an A-a gradient of 5 mm Hg. It outputs the hypoxia symptoms that can manifest as well as the likelihood of different acute mountain sicknesses. 

Commerical aircraft (high pressure differential vehicles) are pressurized between 6,000-8,000 feet, with newer airliners staying on the lower end of 6,000 ft. This makes it very rare for airline passengers to experience any type of mountain sickness symptoms. 

A baseline PaO2 > 70 is generally considered safe for airline travel. Values lower than this will benefit from supplemental O2 during flight. If there is concern, a hypoxia altitude simulation test (HAST) can be performed. This is done by determining the patient’s PaO2 while breathing a gas mixture that recreates the partial pressure of oxygen in flight (85% N2 and 15% O2). If the provoked PaO2 is <55 mm Hg, medical oxygen must be considered.

This calculator uses the hydrostatic loss equation (Ph = 0.78 * h * G) to calculate systolic brain perfusion based on the starting systolic pressure, the aortic valve-to-brain distance, the angle of recline, and the level of +Gz acceleration experienced. On average, every increase in +Gz decreases the systolic perfusion by 30 mm Hg when sitting upright. 

Blackout occurs at an average of 4.8 +Gz for relaxed patients without Anti-G suits with a 1 G/s onset rate, and unconsciousness occurs at an average of 5.4 +Gz. Intraocular pressure, normally 10-20 mm Hg, is subtracted from the brain perfusion pressure to find the ocular perfusion pressure, which is why blackout generally happens prior to unconsciousness. The average G where peripheral light loss occurs is around 4.1 +Gz.

The brain has a 4-6 oxygen reserve time prior to beginning to lose function. However, the baroreceptor reflex takes 6-9 seconds to kick in, with heart level blood pressure restored in 10-15 seconds. This leaves a window where an individual is susceptible to G-LOC, especially after a -Gz maneuver has already reduced cardiac output and blood pressure (the dreaded "push-pull" maneuver).

An Anti-G Straining Maneuver (AGSM) can raise tolerance to +Gz by up to 3 G. Conventional Anti-G suits can raise tolerance by 1-1.5 Gz, with advanced technology anti-G suits (ATAGS) raising tolerance another 0.5-1 Gz. The addition of positive pressure breathing for G (PBG) reduces fatigue from the AGSM and increases aortic pressure, and with the addition of a chest counterpressure garment (jerkin), can sometimes eliminate the need for an AGSM.

This calculator is designed to demonstrate the tyranny of the ideal rocket equation. The calculation assumes a constant acceleration and does not account for factors such as gravity losses or propulsion system inefficiencies. It provides a basic estimate based on the ideal rocket equation.

Delta V examples: 

ISS Low Earth Orbit - 7.8 km/s

Earth escape velocity - 11.2 km/s

Gravity, steering, and atmospheric drag losses are dependent on the duration of launch and can require an additional ~1.5-2 km/s.

Some example specific impulses:

Space Shuttle Solid Rocket Booster - 250 sec
LOX/RP1 @ sea level - 283 sec

LOX/RP1 in vacuum - 312 sec

LOX/Liquid methane @ sea level - 327 sec

LOX/Liquid methane in vacuum - 350 sec

LOX/Liquid Hydrogen - 450 sec

Example payload masses: 

SpaceX dragon capsule - ~ 12,500 kg

Falcon 9 dry weight - ~29,500 kg

Starship LEO payload capacity - ~150,000 kg