1. Mach’s Vision of Flying
P M V Subbarao
Professor
Mechanical Engineering Department
True Understanding of Moving Fast!!!

2. Mach Number : A True Measure of High Speed Systems
Mach number of a flight
Mach number of a Jet

3. Mach’s Cone • Mach Angle
• As Mach number increases, the strength of the Cone increases and the Angle of the shockwave becomes increasingly severe
• Mach Angle

4. Moving Disturbance of Finite Size In A Fluid
• Mach’s thought experiments are limited to infinitesimally small object.
What is minimum size of the object, which will follow Mach’s cone?
Later experience proved following:
As mach number becomes very large for a given size of the object, the Mach wave becomes a shock wave and gets bent so severely that it lies right against the vehicle.
Resulting flow field referred to as a shock layer.

5. Mach’s experiments
Mach was actually the first person in history to develop a method for visualizing the flow passing over an object at supersonic speeds.
He was also the first to understand the fundamental principles that govern supersonic flow and their impact on aerodynamics.
Ernst Mach's photo of a bullet in supersonic flight
"Photographische Fixierung der durch Projektile in der Luft eingeleiten Vorgange" that he presented to the Academy of Sciences in Vienna in 1887.

6. Mach’s Witness of Shock
Not only was Mach was able to make the invisible shock waves visible, but it is even more amazing that he was able to photograph the phenomenon.
His experiments required split-second timing in an age before computers or electronics were available.
Mach's shadowgraph technique and a related method called Schlieren photography are still widely used to observe supersonic flow fields even today.
Yet Mach's contributions to supersonic aerodynamics were not limited to experimental methods alone.
He was the first person to note the sudden and discontinuous changes in the behavior of an airflow when the ratio V/c goes from being less than 1 to greater than 1.

7. Mach Waves, Revisited
• A ‘’point-mass’’ object moving with Supersonic velocity Generates an infinitesimally weak “mach wave”.
The direction of flow remains unchanged across Mach wave.

8. Oblique Shock Wave
• When generating object is larger than a “point”, shockwave is stronger than mach wave …. Oblique shock wave
• -- shock angle
• -- turning or “wedge angle”

9. High Angle Objects Sleek Bodies at supersonic Speeds
Bluff Bodies at supersonic Speeds

10. Mach Number : A Parameter to Select Suitable Flying Technology
Ma <0.2 : Incompressible Flow Systems : Strong Attentions to Laminar & Turbulent Flows : High Cd Systems are economical.
0.2 < Ma <0.9 : Compressible Subsonic Systems : Medium to mild attention to Laminar & Turbulent Flows : Low Cd Systems are essential.
0.9 < Ma <1.05 : Transonic Systems : Better to avoid…
1.05 < Ma < 2.0 : Supersonic Systems : Essential for National Security
Ma > 2.0 : Hypersonic Systems : Means for Space Exploration
Development of An Engineering Science called Gas Dynamics.

11. Evaluation of Speed of A Disturbance in A Medium

12. Conservation Laws Applied to 1 D Steady disturbance
For steady flow momentum equation for CV:
For steady 1-D flow :
p, r ... C
P+dp, r+dr ...
Change = final - initial

13. For infinitesimally small disturbance

14. Travel of sound as A Thermodynamic Process
An infinitesimal disturbance is considered as reversible adiabatic process.
The speed of sound can be obtained easily for an ideal gas because of a simple mathematical expression.
The pressure for a perfect gas during an isentropic process can be expressed as a simple function of density and ratio of specific heats (function of molecular structure ,  namely

15. Role of Speed of Sound in High Speed Flows
Speed of sound in a fluid medium establishes significant interaction between microscopic and macroscopic kinetic energies of the fluid molecules.
Every decelerating molecule will gain microscopic energy and lose macroscopic kinetic energy.
These interactions are understood through definition of Stagnation Properties.
Stagnation property is defined as property of a high speed fluid, when it is isentropically bought to rest.
Stagnation enthalpy, it is defined as the maximum possible microscopic kinetic energy of a fluid.