# Rocket equation with Drag factor

For the avg Thrust of 2 kN,
burn time = 3.5 s,
burn rate= 1.4,
over the time diff of dt = 0.1 sec
Isp = 140 sec
Cd for the Ogive nose cone C-section = 0.75
Cross-sec Area of the ogive nose cone = 0.155 m2.

I am using the equations

Velocity, $$v = I_{sp}\cdot g \cdot ln(m_o/m_f) - g \cdot t$$

acceleration $$a= Thrust/V_(exhaust)$$

height $$h= I_{sp}\cdot g \cdot t \cdot (1-ln(m_o/m_f)/[(m_o/m_f) - 1 ]) - 0.5g\cdot t^2$$

When I add the drag force to this calculation: Can I use the net velocity attained as:

net velocity,$$v_n = v - a_d \cdot t$$

where, deceleration due to drag, $$a_d = Drag-force/mass$$

Similarly, how do I update the equation for the height? Do I just find the net acceleration and use equations of motion instead

$$h= (v^2 - u^2)/(2a_n)$$ an = net acceleration

Thank you all, for being so helpful with responses. I have been stuck for a while on it and the launch is nearing. :)

• If this is a real project I highly recommend OpenRocket for design and simulation Oct 26, 2021 at 11:25
• Thank you @BrendanLuke15 . We are using OpenRocket however, since we are using our own motor, We cannot find a similar rocket in the software to match ours. We can match the weight by adding dummy weight but, then how do you suggest we make up the missing thrust and burn time? Oct 27, 2021 at 7:15
• I believe it's possible to add a custom thrust curve / motor in OpenRocket Oct 27, 2021 at 11:20