Loreal Hair Color Magic Root Rescue is a popular product in the hair dye industry. It is designed to help individuals touch up their roots between salon visits and extend the life of their hair color. Many people struggle with noticeable roots as their hair grows out, and this product offers a convenient solution. The Loreal Hair Color Magic Root Rescue comes in a compact kit that includes a brush and a colorant. The colorant is specifically formulated to match a wide range of hair colors, ensuring a seamless blend with existing hair dye. The brush allows for precise application, making it easy to target only the roots that need touch-up, reducing the risk of staining the rest of the hair.
The block represents the longitudinal forces at the tire-road contact patch using the Magic Formula of Pacejka [2].
When you set Parameterize by to Constant Magic Formula coefficients , the block uses the dimensionless coeffiecients, B , C , D , and E , or stiffness, shape, peak, and curvature, such that. Alternatively, it will convert the kinetic energy into something harmless so she doesn t hurt herself, her allies on the ground, or do any significant property damage.
The brush allows for precise application, making it easy to target only the roots that need touch-up, reducing the risk of staining the rest of the hair. One of the key features of this product is its quick application time. It takes just 10 minutes for the color to process, allowing for a speedy touch-up session.
Tire-Road Interaction (Magic Formula)
The Tire-Road Interaction (Magic Formula) block represents the interaction between the tire tread and the road pavement. The Magic Formula predicts the longitudinal force that results from this interaction by using an empirical equation based on fitting coefficients. The block ignores tire properties such as compliance and inertia.
Tire-Road Interaction Model
The block represents the longitudinal forces at the tire-road contact patch using the Magic Formula of Pacejka [2].
The figure displays the forces on the tire. The table defines the tire model variables.
| Symbol | Description |
|---|---|
| Ω | Wheel angular velocity. |
| rw | Wheel radius. |
| Vx | Wheel hub longitudinal velocity. |
| r w Ω | Tire tread longitudinal velocity. |
| u | Tire longitudinal deformation. |
| V T = r w Ω ′ = r w Ω + u ˙ | Tire tread longitudinal velocity. Typically, the tire tread longitudinal velocity has a component due to tire rotation, rwΩ, and an optional component due to tire deformation, u ˙ . Because port T computes VT, the calculations for tire rotations and deformation occur outside of the block. |
| V s x = V x − V T | Contact patch slip velocity. If there is no tire longitudinal compliance, then u = 0 . |
| k = − V s x | V x | s m o o t h | Wheel slip for a tire without compliance. |
| Fz | Vertical load on tire. |
| Fz0 | Nominal vertical load on tire. |
| F x = f ( k , F z ) | Longitudinal force exerted on the tire at the contact point. f is a characteristic function of the tire. |
Tire Response
You can model tire roll and slip.
Forces and Characteristic FunctionThe block uses a steady-state tire characteristic function, F x = f ( k , F z ) , where:
- Fx is the longitudinal force on the tire.
- Fz is the vertical load.
- k is the wheel slip
The equation for translational motion of a non-slipping, non-compliant tire is V x = r w Ω . When tires experience slip, they develop a longitudinal force, Fx.
The contact patch slip velocity is V s x = V x − r w Ω − u ˙ . For a tire without compliance, u = 0 . The unsmoothed contact patch slip is
and the block saturates the slip denominator as
where VXLOW is the Lower boundary of slip denominator, VXLOW parameter. The block smoothly transitions |Vx| to VXLOW over the transition regions -VXLOW - Vth/2 < Vx < -VXLOW + Vth/2 and VXLOW - Vth/2 < Vx < VXLOW + Vth/2 . The block saturates slip according to
k = < k p u m i n if − V s x | V x | < k p u m i n k p u m a x if − V s x | V x | >k p u m a x − V s x | V x | otherwise
where kpumin is the Minimum valid wheel slip, KPUMIN parameter and kpumax is the Maximum valid wheel slip, KPUMAX parameter. The block transitions k over the regions kpumin - kth/2 < k < kpumin + kth/2 and kpumax - kth/2 < k < kpumax + kth/2 . The block defines the slip smoothing threshold as
k t h = V t h 1 m / s .
For this equation, a locked, sliding wheel has k = -1 . For perfect rolling, k = 0 .
Magic Formula Coefficients for Typical Road ConditionsThe block uses numerical values based on empirical tire data. These values are typical sets of constant Magic Formula coefficients for common road conditions.
| Surface | B | C | D | E |
|---|---|---|---|---|
| Dry tarmac | 10 | 1.9 | 1 | 0.97 |
| Wet tarmac | 12 | 2.3 | 0.82 | 1 |
| Snow | 5 | 2 | 0.3 | 1 |
| Ice | 4 | 2 | 0.1 | 1 |
Parameterizations
Peak Longitudinal Force and Corresponding SlipWhen you set Parameterize by to Peak longitudinal force and corresponding slip , the block uses a representative set of Magic Formula coefficients. The block scales the coefficients to yield the peak longitudinal force Fx0 at the corresponding slip κ0 that you specify, for rated vertical load Fz0.
Magic Formula with Constant CoefficientsWhen you set Parameterize by to Constant Magic Formula coefficients , the block uses the dimensionless coeffiecients, B, C, D, and E, or stiffness, shape, peak, and curvature, such that
F x = f ( κ , F z ) = F z ⋅ D ⋅ sin ( C ⋅ arctan < B κ − E [ B κ − arctan ( B κ ) ] >) .
The slope of f at k = 0 is B C D ⋅ F z .
Magic Formula with Load-Dependent CoefficientsWhen you set Parameterize by to Load-dependent Magic Formula coefficients , the block uses dimensionless coefficients that are functions of the tire load. A more complex set of parameters p_i , entered in the property inspector, specifies these functions:
F x 0 = D x sin ( C x arctan < B x κ x − E x [ B x κ x − arctan ( B x κ x ) ] >) + S V x ,
d f z = ( F z – F z 0 ) F z0
This is especially beneficial for individuals with busy schedules who don't have the time to spend hours at the salon. With the Loreal Hair Color Magic Root Rescue, hair touch-ups can be done in the comfort of one's own home in a fraction of the time. Another advantage of this product is its long-lasting results. The color is designed to stay vibrant and blend naturally for up to three weeks. This ensures that roots remain concealed and hair looks fresh and well-maintained between colorings. Additionally, Loreal Hair Color Magic Root Rescue is resistant to fading and washing out, providing a reliable solution for root regrowth. In terms of application, the process is straightforward. Users simply mix the colorant and developer in a bowl, apply the mixture to the roots using the provided brush, and allow the color to process for 10 minutes. After rinsing, the hair is left with a refreshed and even color, seamlessly blending with the rest of the hair. Overall, Loreal Hair Color Magic Root Rescue provides a convenient and effective solution for individuals looking to touch up their roots and extend the life of their hair color. Its quick application time, long-lasting results, and seamless blend make it a popular choice in the market. With this product, maintaining vibrant and well-groomed hair has never been easier..
Reviews for "The benefits of using Loreal Hair Color Magic Root Rescue on gray hair"
1. Rachel - 2/5 - I was really disappointed with the Loreal hair color magic root rescue. I have some gray roots that I wanted to cover up, but this product just didn't do the job. The color didn't match my hair exactly and it didn't provide enough coverage. It also left my hair feeling dry and brittle. I won't be repurchasing this product.
2. Sarah - 1/5 - This root rescue hair color from Loreal was a total waste of money for me. I followed the instructions carefully, but the color turned out completely different from what was advertised. The roots were still visible and the product didn't blend well with my hair. Moreover, it faded quickly, and within a week, I was back to square one. I would not recommend this product if you're looking for an effective root cover-up.
3. Michelle - 2/5 - I had high hopes for the Loreal hair color magic root rescue, but unfortunately, it fell short of my expectations. The color was easy to apply, but it didn't provide the full coverage I was looking for. It also didn't last very long, and within a couple of washes, my gray roots were visible again. Additionally, the product had a strong chemical smell that lingered in my hair even after I washed it. I wouldn't recommend this to anyone looking for a long-lasting and effective root touch-up solution.
4. Emily - 3/5 - While the Loreal hair color magic root rescue did an okay job of covering up my gray roots, it wasn't anything extraordinary. The color matched decently, but it didn't blend seamlessly with the rest of my hair, leaving a slightly noticeable difference. The product claims to last until the next salon visit, but I found that it started fading after just a couple of weeks. It's an average root cover-up option, but I'm still on the lookout for something better.