Question

For the given set of strand burner data (given also as a .txt for easy excel import):

Calculate the parameters, a and n, of St. Robert’s Law for each T0. Plot the results in log-log space.

Calculate the temperature sensitivity of the propellant, σ_p at P=0.5 MPa, P=5 MPa, and P=10 MPa.

Hypothetical Strand Burner Data
T0=	300	K		T0=	350	K
P (Mpa)	rb (Cm/s)			P (Mpa)	rb (Cm/s)
0.5	2.77E-01			0.5	2.81E-01
1	4.55E-01			1	4.70E-01
1.5	5.66E-01			1.5	5.93E-01
2	6.83E-01			2	7.21E-01
2.5	7.69E-01			2.5	8.39E-01
3	8.68E-01			3	9.70E-01
3.5	9.62E-01			3.5	1.05E+00
4	1.09E+00			4	1.14E+00
4.5	1.18E+00			4.5	1.27E+00
5	1.22E+00			5	1.34E+00
5.5	1.32E+00			5.5	1.45E+00
6	1.37E+00			6	1.54E+00
6.5	1.45E+00			6.5	1.63E+00
7	1.52E+00			7	1.69E+00
7.5	1.59E+00			7.5	1.77E+00
8	1.70E+00			8	1.83E+00
8.5	1.77E+00			8.5	1.91E+00
9	1.79E+00			9	2.00E+00
9.5	1.88E+00			9.5	2.08E+00
10	1.96E+00			10	2.15E+00

Answer 1

from plot slope n = 0.645

log a = -0.359

a = 0.4375 cm/(s-Mpa^n)

slope n = 0.674

a = 0.456 cm/(s-Mpa^n)

Temperature sensivity = d(log r)/dT at const pressure

1) At P = 0.5Mpa, temperature sensivity = 0.0001245 /K

2) At P = 5Mpa, temperature sensivity = 0.000814   /K

3) At P = 10 Mpa, temperature sensivity = 0.0008036    /K