Advanced Question Calculating Average Thrust

[romanasul]

Can somebody explain to me how to calculate the Average Thrust of a Solid Rocket Motor, given the thrust values at different times during the burn. I'm trying to determine the average thrust using these values of time and thrust from a Multistage file:

Curve_1=(0,76)
Curve_2=(2,100)
Curve_3=(4,97)
Curve_4=(6,98)
Curve_5=(22,96)
Curve_6=(52,71)
Curve_7=(76,80)
Curve_8=(110,55)
Curve_9=(120,20)

The value on the left is time after ignition and on the right thrust in percent.

 

[fred18]

you can do a weighted average I think.

so it should be something like multiplying each thrust by its time, summing the results and then summing all times and divide the first for the second, something like sum(thrusts*times)/sum(times)

i did it quite quickly so it could be wrong but my result in your case is 54.8724 % as weighted average.

So if your original thrust is 1000 kN then the average thrust in this curve will be 0.548724*1000 = 54.872,45 kN

---------- Post added at 14:43 ---------- Previous post was at 11:28 ----------

I thought about this again and what I stated above was not 100% right.

Your distribution of thrust is not constant for intervals, but varies linearly.

so you have to compute the average for each interval, the length of each interval and then make the weighted average on those values.

In your case:

first interval:
2 seconds length (2-0) - 88 average ((100-76)/2)+76
second interval:
2 seconds length (4-2) - 98.5 average ((97-100)/2)+100
third interval:
2 seconds length (6-4) - 97.5 average ((98-97)/2)+97)
fourth:
16 secs (22-16) - 97 avg ((96-98)/2)+98)
fifth:
30 secs (52-22) - 83.5 avg ((96-71)/2+96)
sixth:
24 secs (76-24) - 75.5 avg ((71-80)/2+71)
seventh:
34 secs (110-76) - 67.5 avg ((80-55)/2+80)
eight:
10 secs (120-110) - 37.5 avg ((55-20)/2+55)

now the weighted average of the averages for their intervals

so:
numerator= (88*2)+(98.5*2)+(97.5*2)+(97*16)+(83.5*30)+(75.5*24)+(67.5*34)+(37.5*10) = 9107
denominator = total time = 120

average thrust = numerator / denominator = 9107 / 120 = 75.892

so the average thrust of this profile is 75.892 %, if the thrust indicated is 1000 kN, the average thrust will be = 0.75892 * 1000 = 758.92 kN

I think this is right this time, sorry for the first post but I was running a bit.

 

[romanasul]

Thanks again for your help.