View source for Max q

{{DISPLAYTITLE:Max ''q''}}
{{Short description|Aerodynamic phenomenon}}
{{Use dmy dates|date=April 2023}}
{{Other uses}}
[[File:Mercury-Redstone dynamic pressure, The Mercury-Redstone Project NASA TMX 53107.png|thumb|Chart of dynamic pressure during the [[Mercury-Redstone 4]] mission. Max ''q'' occurs 90 seconds after launch, at {{cvt|600|lb/ft2|hPa}}.]]
The '''max <var>q</var>''', or '''maximum dynamic pressure''', condition is the point when an [[aerospace engineering|aerospace]] vehicle's [[atmosphere|atmospheric]] flight reaches the maximum difference between the [[fluid dynamics]] [[Total pressure (fluids)|total pressure]] and the ambient [[static pressure]]. For an [[airplane]], this occurs at the maximum speed at minimum altitude corner of the [[flight envelope]]. For a [[space vehicle]] launch, this occurs at the crossover point between [[dynamic pressure]] increasing with speed and static pressure decreasing with increasing altitude. This is an important design factor of aerospace vehicles, since the aerodynamic [[structural load]] on the vehicle is proportional to dynamic pressure.

==Dynamic pressure==
[[Dynamic pressure]] <var>q</var> is defined in incompressible [[fluid dynamics]] as
<math display="block">q = \tfrac{1}{2} \rho v^2</math>
where ''ρ'' is the local [[air density]], and ''v'' is the vehicle's [[velocity]]. The dynamic pressure can be thought of as the [[kinetic energy]] density of the air with respect to the vehicle, and for incompressible flow equals the difference between [[Total pressure (fluids)|total pressure]] and [[static pressure]].
This quantity appears notably in the [[lift (force)|lift]] and [[drag equation]]s.

For a car traveling at {{convert|56|mph|km/h}} at sea level (where the air density is about {{convert|0.0765|lb/ft3|kg/m3}},<ref>{{Cite web| url=https://www.engineeringtoolbox.com/standard-atmosphere-d_604.html|title=U.S. Standard Atmosphere|access-date=2021-04-24| archive-date=2021-12-22|archive-url=https://web.archive.org/web/20211222213549/https://www.engineeringtoolbox.com/standard-atmosphere-d_604.html|url-status=live}}</ref>) the dynamic pressure on the front of the car is {{convert|0.0555|psi|hPa}}, about 0.38% of the static pressure ({{convert|14.696|psi|hPa}} at sea level).

For an airliner cruising at {{convert|755|ft/s|km/h}} at an altitude of {{convert|33000|ft|km}} (where the air density is about {{convert|0.0258|lb/ft3|kg/m3}}), the dynamic pressure on the front of the plane is {{convert|1.586|psi|hPa}}, about 41% of the static pressure ({{convert|3.84|psi|hPa}}).

==In rocket launches==

For a launch of a [[space vehicle]] from the ground, dynamic pressure is:
* zero at lift-off, when the air density ''ρ'' is high but the vehicle's speed ''v'' = 0;
* zero outside the atmosphere, where the speed ''v'' is high, but the air density ''ρ'' = 0;
* always non-negative, given the quantities involved.

During the launch, the vehicle speed increases but the air density decreases as the vehicle rises. Therefore, by [[Rolle's theorem]], there is a point where the dynamic pressure is maximal.

In other words, before reaching max <var>q</var>, the dynamic pressure increase due to increasing velocity is greater than the dynamic pressure decrease due to decreasing air density such that the net dynamic pressure (opposing kinetic energy) acting on the craft continues to increase. After passing max <var>q</var>, the opposite is true. The net dynamic pressure acting against the craft decreases faster as the air density decreases with altitude than it increases from increasing velocity, ultimately reaching 0 when the air density becomes zero.

This value is significant, since it is one of the constraints that determines the structural load that the vehicle must bear. For many vehicles, if launched at full throttle, the aerodynamic forces would be higher than what they can withstand. For this reason, they are often throttled down before approaching max <var>q</var> and back up afterwards, so as to reduce the speed and hence the maximum dynamic pressure encountered along the flight.

===Examples===
During a normal [[Space Shuttle]] launch, for example, max <var>q</var> value of 0.32 atmospheres occurred at an [[altitude]] of approximately {{cvt|11|km|ft}}, about one minute after launch.<ref name="aeroweb">{{cite web
  | last = Jackson
  | first = Douglas T.
  | title = Space Shuttle Max-Q
  | work = Aerodynamics Questions
  | publisher = AerospaceWeb.org
  | date = 2001-05-06
  | url = http://www.aerospaceweb.org/question/aerodynamics/q0025.shtml
  | accessdate = 2007-02-12
  | archive-date = 2021-11-22
  | archive-url = https://web.archive.org/web/20211122072013/http://www.aerospaceweb.org/question/aerodynamics/q0025.shtml
  | url-status = live
  }}</ref> The three [[Space Shuttle Main Engine]]s were throttled back to about 65–72% of their rated thrust (depending on payload) as the dynamic pressure approached max <var>q</var>.<ref name="NASAblog">{{cite web
  | last = Heiney
  | first = Anna
  | title = Launch Blog
  | publisher = [[NASA]]
  | date = 2007-08-08
  | url = http://www.nasa.gov/mission_pages/shuttle/shuttlemissions/sts118/launch/launch-blog.html
  | accessdate = 2011-05-22
  | archive-date = 2021-11-18
  | archive-url = https://web.archive.org/web/20211118214839/https://www.nasa.gov/mission_pages/shuttle/shuttlemissions/sts118/launch/launch-blog.html
  | url-status = live
  }}</ref> Combined with the propellant grain design of the [[Space Shuttle Solid Rocket Booster|solid rocket boosters]], which reduced the thrust at max <var>q</var> by one third after 50&nbsp;seconds of burn, the total stresses on the vehicle were kept to a safe level.

During a typical [[Project Apollo|Apollo]] mission, the max <var>q</var> (also just over 0.3 atmospheres) occurred between {{convert|13|and(-)|14|km|ft}} of altitude;<ref name="Apollo 8">{{cite web|url=https://history.nasa.gov/ap08fj/01launch_ascent.htm|title=Apollo 8, Day 1: Launch and Ascent to Earth Orbit|last=Woods|first=David|author2=O'Brien, Frank|date=2005-08-21|work=Apollo Flight Journal|publisher=[[NASA]]|archive-url=https://web.archive.org/web/20130702205200/https://history.nasa.gov/ap08fj/01launch_ascent.htm|archive-date=2013-07-02|url-status=dead|accessdate=2007-02-14}}</ref><ref name="Apollo 16">{{cite web|url=https://history.nasa.gov/ap16fj/01_Day1_Pt1.htm|title=Apollo 16, Day One Part One: Launch and Reaching Earth Orbit|last=Brandt|first=Tim|author2=Woods, David|date=2004-10-29|work=Apollo Flight Journal|publisher=[[NASA]]|archive-url=https://web.archive.org/web/20130702201040/http://history.nasa.gov/ap16fj/01_Day1_Pt1.htm|archive-date=2013-07-02|url-status=dead|accessdate=2007-02-14}}</ref> approximately the same values occur for the [[SpaceX]] [[Falcon&nbsp;9]].<ref>{{cite web |title=Starlink Mission (the moment Falcon 9 goes through MAX-Q at an altitude of 12.7 km) |website = [[YouTube]]| date=23 May 2019 |url=https://www.youtube.com/watch?v=riBaVeDTEWI&t=914 |archive-url=https://ghostarchive.org/varchive/youtube/20211219/riBaVeDTEWI |archive-date=2021-12-19 |url-status=live}}{{cbignore}}</ref>

The point of max <var>q</var> is a key milestone during a space vehicle launch, as it is the point at which the airframe undergoes maximum mechanical stress.

== See also ==
* [[Prandtl–Glauert singularity]]
* [[Ideal gas law]]
* [[Gravity turn]]
* [[Gravity loss]]
* [[Equivalent airspeed]] &ndash; max ''q'' for a spacecraft corresponds to maximum equivalent airspeed for an aircraft

== References ==
{{Reflist}}

[[Category:Aerospace engineering]]
[[Category:Fluid dynamics]]