Grade resistance is simply the gravitational force (the component parallel to the roadway) acting on the vehicle. As suggested in Fig. 2.1, the expression for grade resistance (Rg) is
sing gR W θ= (2.8)
As in the development of the rolling resistance formula (Eq. 2.6), highway grades are usually very small, so sin θg ≅ tan θg. Rewriting Eq. 2.8, we get
tang gR W WGθ≅ = (2.9)
G = grade, defined as the vertical rise per some specified horizontal distance (opposite side of the force triangle, Fig. 2.1, divided by the adjacent side) in ft/ft.
Grades are generally specified as percentages for ease of understanding. Thus a roadway that rises 5 ft vertically per 100 ft horizontally (G = 0.05 and θg = 2.86°) is said to have a 5% grade.
A 2000-lb car has CD = 0.40, Af = 20 ft2, and an available tractive effort of 255 lb. If the car is traveling at an elevation of 5000 ft (ρ = 0.002045 slugs/ft3) on a paved surface at a speed of 70 mi/h, what is the maximum grade that this car could ascend and still maintain the 70-mi/h speed?
To maintain the speed, the available tractive effort will be exactly equal to the summation of resistances. Thus no tractive effort will remain for vehicle acceleration (ma = 0). Therefore, Eq. 2.2 can be written as
a rl gF R R R= + +
For grade resistance (using Eq. 2.9),
2000gR WG G= =
for aerodynamic resistance (using Eq. 2.3),
( )( )( )
0.4 20 70 5280 / 3600 2
a D fR C A V ρ=
and for rolling resistance (using Eq. 2.6),
70 5280 3600 0.01 1 2000
rl rlR f W= × = + ×
255 86.22 33.97 2000
0.0674 or a 6.74% grade
= = + + =
Why Work with Us
Top Quality and Well-Researched Papers
Our writers have been trained on how to handle papers placed by our clients. The writer must read and understand before embarking on writing the papers. In case of any issue that needs clarification, writers are encouraged to ask the client or support.
Professional and Experienced Academic Writers
Our team comprises of the best writers and editors. We do thorough vetting during recruitment to make sure that our writers have the knowledge and experience we aspire in the team.
Free Unlimited Revisions
Our aim is to give the client the best outcome. If for some reason you are not satisfied with the wok done, you can ask the paper to be revised or rewritten. This will be done to your satisfaction with no extra charges.
Prompt Delivery and 100% Money-Back-Guarantee
We have writers who work round the clock. This helps in making sure that all our clients’ papers are delivered on time. If we have issues with the deadline, we will ask for extension. If its not possible, the money is fully refunded.
Original & Confidential
Our clients’ confidentiality is highly respected. We can never disclose our clients’ details to third parties. In the same regard, we strive to give our clients 100% original papers. We do not tolerate plagiarism from our writers.
24/7 Customer Support
Clients can reach us any time of the day, and any day of the week. There is a live chat, email or phone numbers to help in ease of communication.
Try it now!
How it works?
Follow these simple steps to get your paper done
Place your order
Fill in the order form and provide all details of your assignment.
Proceed with the payment
Choose the payment system that suits you most.
Receive the final file
Once your paper is ready, we will email it to you.
You should never be worried about your papers even in the middle of the night. Our team will work round the clock to deliver.
We have an able team that can deliver your work in the shortest time possible. The academic level or the type of work should never be a hindrance. Our highly competent support team is always around (24/7) to give you any assistance you may need.
Admission Essays & Business Writing Help
Do you need to be admitted in your dream institution but find it challenging to write an admission essay? Our team is in a position to write the best letter that will guarantee you an admission. We do as well write the best business proposals and reports.
Writing can be fun and enjoyable when everything has been done right. Writing is not just enough without proper editing and proofreading. We have a team of editors that ensure everything falls in place, whether its issues to do with grammar or referencing styles.
Once the paper has been done and submitted, that is not the end of it. You can always ask for amendment or improvement if you feel something has not been done right. Our team of writers and editors will gladly assist you to your satisfaction. Revision is free of charge.