Inverse
Blast Pressure as COVID-Spread in India
Dr
Himanshu Shekhar
Introduction:
When an explosive detonates, a very high pressure is generated at the
point of explosion. The high pressure is spread out in the
surrounding media as blast pressure in all direction from the point
of explosion. The high blast pressure, which is generally stated as
blast peak overpressure (POP) and it attenuates as time and distance
progresses. The actual positive phase of explosion from a blast site
is in microseconds. And the distance to which this blast pressure is
felt may be in tens of meters, depending on explosive quantity and
surrounding media.
Mathematical
Expression for Blast Peak Over Pressure (POP):
The most popular method of expressing the variation of blast POP with
time is the Friedlander waveform. The variation is given by the
following equation.
In
the equation Ps is called stagnation pressure, which is the highest
pressure obtained in an explosion. The t* is critical time, when
pressure becomes zero. However, the blast overpressure (POP continues
to decay to negative side and suction pressure is also created during
any explosion in the affected field. In the explosion surroundings,
it is observed that the buried things come out of ground, after
passage of blast pressure wave. This confirms the nature of the
curve. The curve reaches the lowest value at twice the critical time
and then again rises but remains in negative pressure zone only. The
variation for Ps
= 70 kPa and t* = 100ms, is plotted below.
Simulation
of Covid-Spread:
For the simulation of COVID-spread, the behaviour is entirely
opposite, but has similarity with explosion. The blast peak
overpressure decays with time, but COVID spread increases with time.
In case of COVID spread, initially it is of negligible order, which
rises with passage of time. There is no negative part present in
COVID simulation. To simulate COVID spread, from the blast pressure
curve, following changes are made:
-
The peak pressure is rechristened as COVID peak cases.
-
The intensity of COVID peak is assumed 200000, for simulation.
-
The time period is changed from milliseconds in blast pressure to days in COVID spread.
-
The curve is plotted up to twice the critical time, only.
-
The curve is mirrored in y-axis, shifted along x-axis (rightward) and then along y-axis (upward), to get a curve, similar to COVID spread.
Overall,
if time is expressed in days and peak COVID confirmed cases is
assumed as PCCC, then, number of COVID confirmed cases at any point
of time is given by the following equation.
Simulation
for India:
The cumulative total number of confirmed cases in India on 22.05.2020
is simulated using the modified Friedlander equation, which is used
for simulating blast peak over pressure. The equation is given above
and it has only two variables: one is peak confirmed COVID cases and
second is critical time. In addition to this, simulation is also
using time shift (x-axis shift leftwards). For the simulation PCCC =
1.2 and t* = 18 days, with x shift of 100 days. The superimposed
curve along with actual reported cases on 22.05.2020 is plotted.
The
simulation is made to match and the plot is utilizing that part of
Friedlander equation, which is generally ignored in case of
simulating Blast Peak Overpressure. The curves are going beyond the
peak over pressure value numerically in case of simulating
COVID-cases. The Pearson coefficient of fit is obtained as 0.998.73,
which is a fairly good simulation. From the given equation, it is
predicted that tomorrow, that is on 23.05.2020, 7345 new confirmed
cases will appear in India.
Conclusion:
No doubt, Detonation and COVID-case both are detrimental to human
life and a similarity is explored in the current post. The
Friedlander equation, which is used for the simulation of blast peak
over pressure (POP) from an explosion, is extended to simulate COVID
confirmed cases. A matching curve is obtained and the unexplored part
of the Friedlander equation is utilized for the simulation. From that
data from 10 Feb 2020 to 22 May 2020 is simulated and for tomorrow, 23 May
2020, prediction of 7245 new confirmed cases is made.
Dr Himanshu Shekhar
Very alarming situation. Illiteracy and politics can blast any thing. It is due to both factors. Daily confirm cases of 7250 or like is too much. Let us pray God.
ReplyDeleteThank you. I am just trying to look at numbers from different angles. This is just another way. Numbers are immaterial, but reality matters. Hope for the best.
DeleteKindly derive some equation to predict when the curve is flattening. Else it seems to rise exponentially
ReplyDeleteThanks for comment. Please look at previous posts, where turnaround is also simulated. In fact, after analysing, 11 countries of the world, where turnaround has taken place, analysis is extended to India. Request to please look at those 5 posts. This post is to explore a possibility of explosion type equations for covid spread cases.
DeleteA nice though to use the blast formula for predicting the COVID case.
ReplyDeleteInnovative thought.
Thank you, I think Dr Purabi, one of the scientists, working with explosives. Blast pressure is your domain and COVID is current interest. I appreciate your kind and motivating words. Regards.
ReplyDelete