More physics equations for change in velocity over a time interval with constant acceleration:
(VelocityFinal) = (VelocityInitial) + (Accel) x (Time)
where units for velocity are meters / second
accel is expressed in meters / (second-squared)
and time is in seconds
This gives us a new value for the increased, final velocity at the end of each time interval. As we work our way down the spreadsheet through all the time intervals and keep adding in all those velocity increments we get to a maximum velocity for the rockets entire flight at the end of the motor burn.
Obviously a rocket under thrust has a continuously varying acceleration, but to avoid a whole bunch of calculus (which is a very good thing) I have used a simplified model using the trapezoidal rule and using small time increments (especially during an event like the motor thrust spike where such severe variations occur). Across each 1/100th of a second the final velocity (think of it as final for that time increment) is equal to the initial velocity (which is the final velocity from the previous time increment) plus the delta-V (change in velocity) which is accel x time (which is the duration of the time interval).
The value for delta-V in Column M) is determined by multiplying accel (in Column L) by time (in Column P)
The new total velocity (in column K) comes from adding the previous total velocity (from the line above) to the delta-V
Now that a velocity has been estimated for each time interval it is possible to use this info to estimate the aerodynamic drag force acting on the rocket. Drag force is written in many aero textbooks as:
Drag = (q) x (S) x (cd)
where q is dynamic pressure, calculated as = (1/2) x (air density) x (velocity-squared) and has units of Newtons / (meter-squared)
and S is the frontal or cross-sectional area of the flying object against which the air will scrub and cause drag, with units of meters-squared
cd is the drag coefficient and varies depending on shape and smoothness (cd is a dimensionless, normalized measure)
Air density data can be difficult to find. A quick search at Wiki will give at least one ISA value for sea level, 15 degrees C as (approximately) 1.22521 kg/m3
https://en.wikipedia.org/wiki/Density_of_air
This agrees with the value shown in my old table (1962 NASA standard atmosphere) for sea level, standard day conditions where density (Greek letter rho ) is 0.0023769 slugs/ft3 (conversion using 32.174 pounds per slug, 2.2046 pounds per kilograms, and 3.2808 feet per meter gives a value of 1.225 kg/m3; close enough).
Air density DOES change with altitude (check the standard atmosphere table) but as I stated before a model rocket only reaches a few hundred feet and air density does not change much across this range. I am going to use a constant value, as shown up on line 12.
Dynamic pressure (q) is going to change slightly as the velocity changes for each time increment. A new value is calculated on each line of the flight history and used to estimate a new value of aerodynamic drag for that same line.
So dynamic pressure ( in Column U) is determined by multiplying air density (Row 12, Column D) times velocity squared (Column K) and dividing by 2.
Aerodynamic drag at each line of the flight history is determined by multiplying dynamic pressure (Column U) times the rockets cross-section area (Row 16, Column D) times the drag coefficient (Column R)
With values entered for aerodynamic drag, our estimate of forces acting on the rocket is complete (thrust, drag, and weight) and the acceleration data (Column L) will now show a finished set of data. According to this estimate of model rocket performance, my design undergoes some 44 gs of acceleration at the moment of peak thrust. (Lets see those high-power guys top THAT!)
View attachment 11_delta-v_and_velocity_step_06.xlsx